COMP- BANKING ETC

NUMBER SYSTEM 

EXERCISE -A

1) Find the place value of 2 in 832567

a) 200 b) 2 c) 2000 d) 20000

2) Which one is a rational number?

a) √4 b) √3 c) 2 + √3 d) 5 √3

3) The reciprocal of the sum of reciprocals of 7/6 and 1/9 is

a) 17/69 b) 7/69 c) 27/69 d) 37/69

4) The sum of a non-zero number and ten times its reciprocal is 7. Find the number 

a) 4 b) 3 c) 5 d) 6

5) If 4/5th of 6/7th of a number is 216, then 8/9th of that number will be 

a) 179 b) 280 c) 160 d) 269

6) If 6/7 of 8/5th of a number is 192, then 3/4th of that number is 

a) 105 b) 77 c) 36 d) 80

7) When 0.090909..... is converted into a fraction, then the result is 

a) 1/33 b) 1/11 c) 2/33 d) 6/11

8) The fractions in descending order are 

a) 7/9,5/7,3/5 b) 7/9, 3/5, 5/7 c) 3/5, 5/7, 7/9 d) none 

9) The fractions in ascending order are 

a) 4/15,5/17,10/33,8/27

b) 5/17,10/33,8/27, 4/25

c) 4/15,5/17,8/27, 10/33

d) 10/33,8/27, 5/17,4/15

10) Which one is an irrational number?

a) 22/7 b) π c) 1.333 d) 3.14

11) The smallest odd number is 

a) 0 b) 1 c) 2 d) 3

12) The sum of all prime numbers between 30 and 42 is

a) 103 b) 109 c) 105 d) 104

EXERCISE -2

1) Find the number of zeroes in the factorial of the number 18.        3

2) Find the number of zeroes in 27!.            6

3) Find the number of zeroes in 137!.           33

4) Find the number of zeroes in 

a) 81!              19

b) 100!            24

c) 51!               12

5) What exact power of 5 divides 87!.        20

6) What power of 8 exactly divides 25!        7

7) What power of 15 divides 87! exactly.         20

8) What power of 30 will exactly divide 128!      

9) What power of 210 Will exactly divide 142!.

10) Find the last digit in the expression (36472)¹²³! x 34767⁷⁶!.   6

11) Find the number of numbers between 100 to 200 if

a) both 100 and 200 are counted.       101

b) Only one of 100 and 200 counted.     100

c) Neither 100 not 200 is counted.     99

12) Find the number of even numbers between 122 and 242 id:

a) both ends are included.     61

b) only one end is included.     60

c) Neither end is included.       59

13) Find the number of numbers between 140 to 259, both included, which are divisible by 7.

14) Find the number of numbers between 100 to 200, which are divisible by 3.

15) Find the number of numbers between 300 to 400(both included), that are not divisible by 2,3,4,5.       101

16) Find the number of numbers between 100 to 400, which are divisible by either 2,3,5,7.

17) Find the number of zeroes in the following multiplication:

5× 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50.       8

18) Find the remainder for [(73×79×81)/11].    1

19) Find the remainder for 3⁵⁶⁰/8.       1

20) Find the remainder when (2222⁵⁵⁵⁵ + 5555²²²²)/7.       0

21) Find the GCD and LCM of the numbers 126, 540, 630.    18,3780

22) Find the GCD and LCM of the following numbers:

a) 360,8400.

b) 120,144.

c) 275,180,372,156.    

d) 70,112.

e) 75,114

f) 544,720.

23) The ratio of the factorial of a number x to the square of the factorial of another number, which when increased by 50% gives the required number, is 1.25. find the number x.     

a) 6 b) 5 c) 9 d) none       a

24) Three numbers A,B,C are such that the difference between the highest and the second highest two digit numbers formed by using two of A, B and C is 5. If B> A > C then what is the value of B?

a) 1 b) 6 c) 7 d) 8          d

25) Find the remainder when 2851 x (2862)² x (2873)² is divided by 23.       18

26) For what maximum value of n will the expression 10200!/504ⁿ be an integer?     1698

27) Find the units digit of the expression:

78⁵⁵⁶² × 56²⁵⁶ × 97¹²⁵⁰.        6

28) Find the GCD and LCM of the numbers P and Q where P= 2³× 5³× 7² and Q= 3³× 5⁴.   5³, 2³×3³×5⁴×7²

29) A school has 378 girl students and 675 boy students. The school is divided into strictly boys or strictly girls sections. All sections in the school have the same number of students. Given this information, what are the number of sections in the school.    39

SAP-3

1) The last digit of the number obtained by multiplying the numbers 81× 82 × 83 ×84 × 85 × 86 × 87 × 88× 89

a) 0 b) 9 c) 7 d) 2

2) The sum of the digits of a two digit number is 10, while when the digits are reversed, the number decreases by 54. Find the changed number.

a) 28 b) 19 c) 37 d) 46

3) When we multiply a certain two digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits by the sum of the digits, we get 486. Find the number.

a) 81 b) 45 c) 36 d) none

4) The sum of two numbers is 15 and their geometric mean is 20% lower than their arithmetic mean. Find the numbers.

a) 11,4 b) 12,3 c) 13,2 d) 10,5

5) The difference between two numbers is 48 and the difference between the arithmetic mean and the geometric mean is two more than half of 1/3 of 96. Find the numbers.

a) 49,1 b) 12,60 c) 36,84 d) none 

6) If A381 is divisible by 11, find the value of of the smallest natural number A?

a) 5 b) 6 c) 7 d) 9

7) If 381A is divisible by 9, find the value of smallest natural number A?

a) 5 b) 6 c) 7 d) 9

8) What will be the reminder obtained when (9⁵+1) will be divided by 8?

a) 0 b) 3 c) 7 d) 2

9) Find the ratio between the lcn and HCF of 5,15 and 20

a) 8:1 b) 14:3 c) 12:2 d) 12:1

10) Find the LCM of 5/2, 8/9, 11/14.

a) 280 b) 360 c) 420 d) none 

11) If the number A is even, which of the following will be true?

a) 3A will always be divisible by 6.

b) 3A+5 will always be divisible by 11.

c) (A²+3)/4 will be divisible by 7.

d) none 

12) A five digit number is taken. Sum of the first four digits (excluding the number at the unit digit) equals sum of all the five digits. Which of the following will not divide this number necessarily.

a) 10 b) 2 c) 4 d) 5

13) A number 15B is divisible by 6. Which of these will be about the positive integer B ?

a) B will be even 

b) B will be odd

c) B will be divisible by 6

d) both a and c 

14) Two numbers P= 2³. 3¹⁰. 5 and Q= 2³. 3¹. 7¹ are given. Find the GCD of P and Q.

a) 2.3.5.7 b) 3.2² c) 2².3² d) 2³.3

15) Find the units digit of the expression 25⁶²⁵¹ + 36⁵²⁸+ 73⁵⁴

a) 4 b) 0 c) 6 d) 5

16) Find the units digit of the expression 55⁷²⁵+ 73⁵⁸¹⁰ + 22⁸⁵³.

a) 4 b) 0 c) 6 d) 5

17) Find the units digit of the expression 11¹+ 12²+ 13³+ 14⁴+ 15⁵+ 16⁶

a) 1 b) 9 c) 7 d) 0

18) Find the units digit of the expression 11¹. 12². 13³. 14⁴. 15⁵. 16⁶.

a) 4 b) 0 c) 7 d) none 

19) Find the number of zeroes at the end of 1090!

a) 270 b) 268 c) 269 d) none 

20) If 146! us divisible by 5ⁿ, then find the maximum value of n.

a) 34 b) 35 c) 36 d) 37

21) Find the number of divisors of 1420.

a) 14 b) 15 c) 13 d) 12

22) Find the HCF and LCM of the polynomials (x² - 5x +6) and (x² - 7x +10).

a) (x -2), (x -2), (x -3), (x -5).

b) (x -2), (x -2), (x -3)

c) (x -2), (x -2), (x -3), (x -5) d) none 

* Directions for 23-25: Given two different prime numbers P and Q, find the number of divisors of the following:

23) P. Q

a) 2 b) 4 c) 6 d) 8

24) P². Q

a) 2 b) 4 c) 6 d) 8

25) P³ Q²

a) 2 b) 4 c) 6 d) 12

26) The sides of a pentagon field (not regular) are 1737 metres, 2160 m, 2358 m, 1422m and 2214m respectively. Find the greatest length of the tape by which the five sides may be measured completely?

a) 7 b) 13 c) 11 d) 9

27) There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections this formed?

a) 24 b) 32 c) 16 d) none 

28) A milkman has three different qualities of milk. 403 gallons of 1st quality, 465 gallons of 2nd quality and 496 gallons of 3rd quality. Find the least possible number of bottles of equal size in which different milk of different qualities can be filled without mixing?

a) 34 b) 46 c) 26 d) 44

29) What is the greatest number of 4 digits that when divided by any of the numbers 6,9,12,17 leaves a reminder of 1?

a) 9997  b) 9793 c) 9895 d) 9487

30) Find the least number that when divided by 16,18,20 leaves a reminder 4 in each case, but is completely divisible by 7.

a) 364 b) 2254 c) 2884 d) 3234

31) Four bells ring at the intervals of 6,8,12 and 18 seconds. They start ringing together at 12'o clock. After how many seconds will they ring together again?

a) 72 b) 84 c) 60 d) 48

32) For question 31 find how many times they will ring together during the next 12 minutes?

a) 9 b) 10 c) 11 d) none 

33) The units digit of the expression 125⁸¹³ x 553³⁷⁰³ x 4532⁸²⁸ is 

a) 4 b) 2 c) 0 d) 5

34) Which of the following is not a perfect square?

a) 100856 b) 325137 c) 944729 d) all of these

35) Which of the following can never be in the ending of a perfect square?

a) 6 b) 00 c) 000 d) 1

36) The LCM of 5,8,12,20 will not be a multiple of 

a) 3 b) 9 c) 8 d) 5

37) Find the number of divisors of 720 (including 1 and 720).

a) 25 b) 28 c) 29 d) 30

38) The LCM of (16 - x²) and (x² + x -6) is 

a) (x -3)(x +3)(4- x²)

b) 4(4- x²)(x +3)

c) (4- x²)(x -3) d) none 

39) OCD of x² -4 and x² + x - 6 is

a) x+2 b) x -2 c) x² -2 d) x² + 2

40) The number A is not divisible by 3. Which of the following may not be divisible by 3?

a) 9A b) 2 x A c) 18 x A d) 24 x A

41) Find the remainder when the number 9¹⁰⁰ is divided by 8?

a) 1 b) 2 c) 0 d) 4

42) Find the number 2¹⁰⁰⁰ is divided by 3?

a) 1 b) 2 c) 4 d) 6

43) Decompose the number 20 into two terms such that their product is the greatest.

a) x₁ = x₂= 10

b) x₁=5, x₂= 15

c) x₁= 8, x₂= 12  d) none 

44) Find the number of zeros at the end of 50 !

a) 13 b) 11 c) 5 d) 12

45) Which of the following can be a number divisible by 24 ?

a) 4,32,15,604 b) 25,61,284 c) 1362480 d) none 

46) For a number to be divisible by 88, it should be

a) divisible by 22 and 8 

b) divisible by 11 and 8 

c) divisible by 11 and thrice by 2 

d) both b and c

47) Find the number of divisors of 10800.

a) 57  b) 60 c) 72  d) none 

48) Find the GCD of the polynomials (x +3)²(x -2)(x + 1)² and (x +1)³(x+3)(x+4).

a) (x+3)³(x+1)²(x -2)(x+4)

b) (x+3)(x+1)(x -2)(x+4)

c) (x+3)(x+1)² d) none 

49) Find the LCM of (x+3)(6x²+5x+4)(2x²+ 7x +3)(x+3)

a) (2x+1)(x+3)(3x +4)

b) (4x²-1)(x+3)²(3x +4)

c) (4x²-1)(x+3)(3x +4)

d) (2x-1)(x+3)(3x +4)

50) The product of three consecutive natural numbers, the first of which is an even number, is always divisible by 

a) 12 b) 24  c) 6  d) all of these 

51) Some birds settled on a branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two a branch and there was one branch too many. How many branches were there ?

a) 3 b) 4 c) 5 d) 6

52) The square of a number greater than 1000 that is not divisible by 3, when divided by three, leaves a remainder of 

a) 1 always b) two always c) either one or two d) cannot be said

53) The value of the expression (15². 21²)/(35².3⁴) is 

a) 3 b) 15 c) 21 d) 12

54) If A= (-3/4)³, B= (-2/5)², C= (0.3)², D= (-1.2)² then

a) A> B> C> D b)  D> A> B> C c) D> B> C > A d) D> C> A> B

55) If 2< x < 4 and 1< y < 3, then find the ratio of the upper limit for x+ y and the lower limit of x - y.

a) 6 b) 7 c) 8 d) none 

56) The sum of the square of the digits constituting a positive two digit number is 13. if we subtract 9 from that number, we shall get a number written by the same digits in the reverse order. Find the number ?

a) 12 b) 32 c) 42  d) 52 

57) The product of a natural number by the number written by the same digits in the reverse order is 2430. Find the numbers.

a) 54 and 45  b) 56 and 65 c) 53 and 35 d) none 

58) Find two natural numbers whose difference is 66 and the least common multiple is 360.

a) 120 and 54 b) 90 and 24 c) 180 and 114 d) none 

59) find the pair of natural numbers whose least common multiple is 77 and the greatest common divisor is 13.

a) 58 and 13 or 16 and 29

b) 68 and 23 or 36 and 49

c) 18 and 73 or 56 and 93

d) 78 and 13 or 26 and 39

60) Find two natural numbers whose sum is 85 and the least common multiple is 102.

a) 30 and 55 b) 17 and 68 c) 35 and 55 d) 51 and 34

61) Find the pairs of the natural numbers the difference of whose square is 55.

a) 28 and 27 or 8 and 3 

b)18 and 17 or 18 and 13

c) 8 and 27 or 8 or 33  d) none 

62) Which of these is greater

a) 54⁴ or 21¹² b) (0.4)⁴ or (0.8)³

63) is it possible for a common fraction whose numerator is less than the denominator to be equal to a fraction whose numerator is greater than denominator?

a) yes b) no

64) When digit should be put in place of c in 38c to make it divisible by 

a) 2 b) 3 c) 4  d) 5 e) 6 f) 9 g) 10

65) Find the LCM and HCF of the following numbers:  (54,81, 135 and 189l, (156, 195) and (1950, 3900)

1a 2a 3b 4b 5a 6c 7b 8d 9d 10d 11a 12c 13c 14d 15b 16c 17b 18b 19a 20b 21d 22a 23b 24c 25d 26d 27c 28d 29b 30c 31a 32b 33c 34d 35c 36b 37d 38d 39b 40b 41a 42a 43a 44d 45c 46d 47b 48c 49c 50d 51a 52a 53b 54c 55d 56b 57a 58b 59d 60d 61a 

SAP- 4

1) The arithmetic mean of two number is smaller by 24 than the larger of the two numbers and the GM of the same number exceeds by 12, the smaller of the numbers. Find the numbers.

a) 6 and 54 b) 8 and 56 c) 12 and 60 d) 7 and 55

2) Find the number of numbers between 200 and 300, both included, which are not divisible by 2, 3, 4 and 5.

a) 27 b) 26 c) 25 d) none 

3) given x and n are integers, (15n³+ 6n²+ 5n +x)/n is not an integer for what condition ?

a) n is positive

b) x is divisible by n

c) x is not divisible by n

d) a and c

4) The unit digit in the expression 36²³⁴. 33⁵¹². 39¹⁸⁰. 54²⁹. 25¹²³. 31⁵¹² will be 

a) 8 b) 0 c) 6 d) 5

5) The difference of 10²⁵ - 7 and 10²⁴ + x is divisible by 3 for x=?

a) 3 b) 2 c) 4 d) 6

6) Find the value of x is 

√[x + 2√{x + 2 √(x + 2 √3x )}]= x.

a) 1 b) 3 c) 6 d) 12

7) if a number is multiplied by 22 and the same number is added to it, then we get a number that is half the square of that number. Find the number

a) 45 b) 46 c) 47  d) data insufficient 

8) 12⁵⁵/3¹¹ + 8⁴⁸/16¹⁸ will give in the digit at units place as 

a) 4 b) 6  c) 8 d) 0 

9) The mean of 1, 2, 2²,.....2³¹ lies in between 

a) 2²⁴ to 2²⁵ b) 2²⁵ to 2²⁶ c) 2²⁶ to 2²⁷ d) 2²⁹ to 2³⁰.

10) xy is a number that is divided by ab where xy< ab and gives a result 0xyxyxy.....then ab equals

a) 11 b) 33 c) 99 d) 66

11) A number xy multiplied by another number ab and the result comes as pqr ,  where r= 2y, q=2(x + y) and p= 2x where x, y< 5, q≠ 0. The value of ab maybe

a) 11 b) 13 c) 31 d) 22

12)  [x] denotes the greatest integer value just below x [x] its fractional value. The sum of [x]² and [x]² is -7.91. Find x.

a) -2.03 b) -1.97 c) 2.97 d) -1.7

13) 16⁵+ 2¹⁵ is divisible by 

a) 31.p b) 13 c) 27 d) 33

14) If AB+ XY = 1 XP, where A≠0 and all the letters signify different digits from 0 to 9, then the value of A is 

a) 6 b) 7 c) 9 d) any value above 6

* Directions questions 15-16

Find the possible integral values of x.

15) |x - 3|+ 2|x +1|= 4

a) 1 b) -1 c) 3  d) there are many solutions 

16) x²+ |x -1|= 1

a) 1 b) -1 c) 0 d) 1 or 0

17) If 4ⁿ⁺¹ + x and 4²ⁿ - x are divisible by 5, n being an even integer, find the least value of x.

a) 1 b) 2 c) 3 d) none 

18) If the sum of the numbers (a25)² and a³ is divisible by 9, then which of the following may be a value for a ?

a) 1 b) 7 c) 9 d) there is no value 

19) If |x +4| + |y -4|= 4, then how many integer values can the set (x,y) have?

a) infinite b) 5 c) 16 d) 9 

20) [3³²/50] gives remainder and [.] denotes the fractional part of that. The fractional part is of the form (0. bx). The value of x could be 

a) 2 b) 4 c) 6 d) 8

21) The sum of two numbers is 20 and their geometric mean is 20% lower than their arithmetic mean. Find the ratio or the numbers .

a) 4:1 b) 9 :1 c) 1: 1 d) 17:3 

22) The power on 990 that will exactly divide 1090! is 

a) 101 b) 100 c) 108 d) 109 

23) if 146! is divisible by 6ⁿ, then find the maximum value of n.

a) 74 b) 70 c) 76  d) 75 

24) The last two digits in the multiplication of 35. 34. 33. 32. 31. 30. 29. 28. 27.26 is 

a) 00 b) 40 c) 30 d) 10 

25) The expression 333⁵⁵⁵+ 555³³³ is divisible by 

a) 2 b) 3 c) 37 d) all of these 

26) [x] denote the greatest integer value just below x and [x] its fractional value. The sum of [x]² and [x]¹ is 25.16 . Find x.

a) 5.16  b) -4.84 c) both a and b d) cannot be determined 

27) if we add the square of the digit in the tens place of a positive two-digit number to the product of the digits of that number, we shall get 52, and if we add the square of the digit number in the units place to the same product of the digits, we shall get 11?  Find the two digit number.

a) 18 b) 39 c) 49 d) 28

28) Find two numbers such that their sum, their product and the difference of their squares are equal.

a) {3+√3)/2} and {(1+√2)/2} or {3+√2)/2} and {(1+√2)/2}

b) {3+√7)/2} and {(1+√7)/2} or {3+√6)/2} and {(1-√6)/2}

c) {3-√5)/2} and {(1-√5)/2} or {3+√5)/2} and {(1+√5)/2} d) none 

29) The sum of the digits of a three digit number 17, and the sum of the squares of its digits is 109. If we subtract 495 from the remainder, we shall get a number consisting of the same digits written in the reverse order. Find the number.

a) 773 b) 863  c) 683 d) 944 

30) Find the number of zeros in the product 1¹x 2² x3³ x 4⁴ x ...98⁹⁸ x 99⁹⁹ x 100¹⁰⁰

a) 1200 b) 1300 c) 1050 d) none

31) Find the pairs of a natural number whose greatest common divisor is 5 and the least common multiple is 105.

a) 5 and 150 or 14 and 35

b) 6 and 150 or 16 and 35

c) 5 and 15 or 15 and 135 d) none 

32) The denominator of an irreducible fraction is greater than the numerator by 2. if we reduce the numerator of the reciprocal fraction by 3 and subteact the given fraction from the resulting one, we get 1/15. Find the given fraction 

a) 2/4 b) 3/5  c) 5/7  d) 7/9

33) A two digit number exceeds by 19 the sum of the squares of its digits and by 44 the double product of its digits , find the number 

a) 72 b) 62 c) 22 d) 12

34) The sum of the squares of the digits constituting a two digit positive numbers is 2.5 times as large as the sum of its digits and is large by unity than the trebled product of its digits. Find the number.

a)  13 and 31 b) 12 and 21 c) 22 and 33 d) 14 and 41

35) The unit digits of a two digit number is greater than its tens digit by 2, and the product of that number by the sum of its digit is 144. Find the number.

a) 14 b) 24 c) 46 d) 35

36) Find the number of zeros in the product 5 x 10 x 25 x 40 x 50 x 55 x 65 x 125 x 80.

a) 8 b) 9 c) 12 d) 13

37) The power of 44 that will exactly divided by 123! is

a) 29 b) 30 c) 31 d)!59 

38) three numbers are such that the second is as much lesser than the third as the first is lesser than the second. if the product of the two smaller number is 85 and the product of two larger numbers is 115, find the middle number.

a) 9 b) 8 c) 10 d) 30

39) Find the smallest natural number n such that n! is divisible by 990.

a) 3 b) 5 c) 11 d) none 

40) √x √y= √(xy) is true when 

a) x> 0, y> 0 b) x> 0 and y< 0 c) x< 0 and y >0 d) all of these 

41) find the two digit number that meets the following criteria. If the number in the units place exceeds , the number in its tens by 2 and the product of the digit of a digit number is twice as the sum of a digit free subscription from the required number with the sum of its digits is equal to 144.

42) The product of the digits of a two digit number is twice as large as the sum of its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number ?

43) The product of the digits of a two digit number is one third that number. if we add 18 to the required number, we get a number consisting of the same digits written in the reverse order. Find the number ?

44)  The sum of the squares of the digits of a two digit number is 13. If we subtract 9 from the number, we get a number consisting of the same digits written in reverse order. Find the number?

45) A two digit number 13 is thrice as large as the sum of its digits, and the square of that sum is equal to trebled required number. Find the number ?

46) Find a two digit number that exceeds by 12, the sum of the squares of its digits and by 16 the doubled product of the digits.

47) The sum of the squares of the digits containing a two digit number is 10, and the product of the required number by the number consisting of the same digits written in the reverse order is 403. Find the 2 numbers that satisfy these conditions?

48) If we divide a two digit number by the sum of its digits , we get 4 as a quotient and 3 as remainder. Now, if we divide that two digit number by the product of its digits , we get 3 as a quotient and 5 as a remainder. Find the two digit number.

49) There is a natural number that will becomes equals to the square of a natural number when 100 is added to it. and to the square of another natural number when 169 is added to it. Find the number ?

50) Find two natural numbers whose sum is 85 and whose least common multiple is 102.

51) Find two-three digit numbers whose sum is a multiple of 504 and the quotient is a multiple of 6.

52) The difference between the digits in a 2-digit number is equals to 2, and the sum of the squares of the same digit is 52. Find all the possible numbers?

53) if we divide a given two digit number by the product of its digits , we obtain 3 as a quotient and 9 as a remainder. if we subtract the product of the digits constituting the number, from the square of its digits, we obtain the given number. Find the number.

54) Find the three-digit numbers if it is known that the sum of its digit is 17 and the sum of the square of its digits is 109. If we subtract 495 from this number, we obtain a number consisting of the same digits written in reverse order.

55) The sum of the cubes of the digits constituting a two digit number is 243 and the product of the sum of its digits by the product of its digits is 162. Find the two two-digit number ?

56) The difference between two numbers is 16. What can be said about the total numbers divisible by 7 that can lie between these two numbers.

57) Arrange the following in descending order:

111⁴, 110.108.108.107, 109.110.112.113

58) If 3≤ x ≤ 5 and 4 ≤ y ≤ 7. Find the greatest value of xy and the least value of x/y.

59) Which of these is greater:

a) 200³⁰⁰ or 300²⁰⁰ or 400¹⁵⁰

b) 5¹⁰⁰ and 2²⁰⁰

c) 10²⁰ and 40¹⁰

60) The sum of the two numbers is equal to 15 and their arithmetic mean is 25% greater than its geometric mean. Find the numbers.

31a 32b 33a 34a 35b 36b 37a 38c 39c 40a 41) 24 43) 63 44) 32 45) 27 46) 64 47) 13,31 48) 23 49) 1056 50) 51,34 51) 144,864 52) 46,64 53) 63 54) 863 55) 36,63 56) may be 2 or 3 depending upon the number 57) 111⁴> 109.110.112.113> 110.109.108.107 58) greatest --> 35 least 3/7

59)    60) 12,3

SAP-5

1) What two- digit number is less than the sum of the square of its digits by 11 and exceed their doubled product by 5 ?

a) 15, 95 b) 95 c) both a and b d) 15, 95 and 12345

2) Find the lower other two successive natural numbers if the square of the sum of those numbers exceed the sum of the squares by 112

a) 6 b) 7 c) 8 d) 9 

3) First we increased the denominator of a positive fraction by 3 and then we decreased it by 5. The sum of the resulting fractions proves to be equals to 2/3. Find the denominator of the fraction if its numerator is 2.

a) 7 b) 8 c) 13 d) 9

4) Find the last two digits of: 15 x 37 x 63 x 51 x 97 x 17.

a) 35 b) 45 c) 55 d) 85

5) Let us consider a fraction whose denominator is smaller than the square of the numerator by unity. if we add 2 to the numerator and the denominator, the fraction will exceed 1/3. If we subtract 3 from the numerator and the denominator, the fraction will be positive but smaller 1/10. Find the value ?

a) 3/8  b) 4/15  c) 5/24 d) 6/35

6) Find the sum of all three digit numbers that give a remainder of 4 when they are divisible by 5.

a) 98720 b) 99270 c) 102090 d) none 

7) Find the sum of all two digit number that give a remainder of 3 when they are divided by 7.

a) 686 b) 676 c) 666 d) 656

8) Find the sum of all odd three digit numbers that are divisible by 5.

a) 50500 b) 50250 c) 50000 d) 49500

9) The product of a two digit number by a number consisting of the same digits written in the reverse order is equal to 2430. Find the lower number.

a) 54 b) 45 c) 63 d) 65

10) Find the lowest of three numbers as described. If the cube of the first number exceeds their product by 2, the cube of the second number is smaller than their product by 3, and the cube of the third number exceeds their product by 3.

a) 3¹⁾³ b) 9¹⁾³ c) 2 d) any of these 

11) How many pairs of natural numbers are there the difference of whose squares is 45.

a)  1 b) 2 c) 3 d) 4

12) Find all two digit numbers such that the sum of the digits constituting the number is not less than 7, the sum of the squares of the digits is not greater than 30; the number consisting of the same digits in the reverse order is not larger than half the given number 

a) 52 b) 51 c) 49  d) 53

13)  in a four digit number, the sum of the digits in the thousands, hundreds and tens is equal to 14, and the sum of the digits in the units , tens and hundreds is equal to 15. Among the numbers satisfying these conditions , find the number the sum of the squares of whose digits is the greatest.

a) 2572 b) 1863 c) 2573 d) none 

14) in a four digit number, the sum of the digits in the thousands and tens is equal to 4,  the sum of the digits in the 1000 in the hundreds and the units is 15, and the digit of the units exceeds by 7 the digit of the thousands. Among all the numbers satisfying these conditions , find the number the sum of the product of whose digit of the thousands by the digit of the units and the product of the digit of the hundreds by that of the tens assumes the least value.

a) 4708 b) 1738 c) 2629 d) none 

15) If we divide a two digit number by a number consisting of the same digits written in the reverse order, we get 4 as a quotient and 15 as a reminder. if we subtract 1 from the given number, we get the sum of the squares of the digit consisting that number. Find the number ?

a)  71 b) 83 c) 99 d) none 

16) Find the two digit number the quotient of whose division by the product of its digit is equal to 8/3, and the difference between the required number and the number consisting of the same digits written in the reverse order is 18

a) 86 b) 42 c) 75  d) none 

17) Find the two digit number if it is known that the ratio of the required number and the sum of its digits is 8 as also quotient of the product of its digits and the sum is 14/9

a) 54 b) 72 c) 27 d) none 

18) if we divide the unknown two digit number by the number consisting of the same digits written in the reverse order, we get 4 as a quotient and 3 as a remainder. if we divide the required number by the sum of its digits , we get 8 as a quotient and 7 as a remainder. Find the number ?

a) 81 b) 91 c) 71  d) none 

19) The last two digits in the multiplication 122 x 123 x 125 x 127 x129 will be 

a) 20 b) 50 c) 30 d) 40

20) the remainder obtained when 43¹⁰¹ x 23¹⁰¹ is divided by 66 is

a) 2 b)10 c) 5 d) 0 

21) The last 3 digits of the multiplication 12345 x 54 321 will be 

a) 865  b) 745 c) 845  d) 945

22) The sum of the digits of a three digit number is 12. If we subtract 495 from the number consisting of the same digits written in reverse order, we shall get the required number. Find that three-digit number if the sum of all pairwise products of the digits consisting the number is 31.

a) 156 b) 237 c) 197 d) both a and b 

23) A 3 digit positive integer abc is such that a²+ b⅖ + c² = 74. a is equal to the doubled sum of the digits in the tens units places. Find the number if it is known that the difference between that number and the number written by the same digits in the reverse order is 495

a) 813  b) 349  c) 613  d) none 

24) Represent the number 1.25 as a product of three positive factors so that the product of the first factor by the square of the second is equal to 5 if we have to get the lowest possible sum of three factors.

a) x₁= 2.25, x₂= 4, x₃= 0.2

b) x₁= 1.25, x₂= 4, x₃= 4.5

c) x₁= 1.25, x₂= 2, x₃= 0.5 d) none 

25) Find number x such that the sum of that number and its square is the least 

a) -0.5  b) 0.5 c) -1.5 d) 1.5 

26) When 2222⁵⁵⁵⁵+ 5555²²²² is divided by 7, the remainder is 

a) 0 b) 2 c) 4 d) 5 

27) If x is a number of 5-digits which when divided by 8, 12, 15, 20 leaves respectively 5, 9, 1200,17 as remainders, then find x such that it is the lowest such number ?

a) 10017 b) 10057 c) 10097 d) 10137

28) 2²ⁿ -1 is divisible by 2ⁿ⁺³  for n=

a) 1 b) 2 c) 3 d) none 

29) ip10ⁿ - (5+ √17)ⁿ is divisible by 2ⁿ⁺¹ for what whole number value of n ?

a) 2 b) 3 c) 7  d) never 

30)  (₃₂32³²)/9 will leave a reminder 

a) 4 b) 7 c) 1 d) 2 

31) Find the reminder for the number 1989.1990.1992³ gives when divided by 7

a) 0 b) 1 c) 5 d) 2

32) Find the reminder 2¹⁰⁰ when divided by 3.

a) 3 b) 0 c) 1 d) 2

33) Find the remainder 3¹⁹⁸⁹ is divided by 7.

a) 1 b) 5 c) 6 d)  4

34)  Find the last digit of the number 1²+ 2² + ....99². 

a) 0 b) 1 c) 2 d) 3

35) Find GCD (2¹⁰⁰ -1, 2¹²⁰ -1).

a) 2²⁰ -1 b) 2⁴⁰ -1 c) 2⁶⁰ -1 d) 1¹⁰ -1

36) Find the GCD (111.......11) hundred ones; 11.....11 sixty ones).

a) 111.......forty ones

b) 111.....twenty ones

c) 1111.....twenty ones

d) none of these 

37) Find the last digit of the number 1³+ 2³+ 3³ + 4³....+99³

a) 0 b) 1 c) 2 d) 5

38) Find the GCD of the numbers 2n+13 and n+7.

a) 1 b) 2 c) 3 d) 4

39) (₃₂32³²)/7

a) 4 b) 2 c) 1 d) 3

40) The remainder when 10¹⁰+ 10¹⁰⁰+ 10¹⁰⁰⁰+ ....+ 10¹¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ is divided by 7 is

a) 0 b) 1 c) 2 d) 5

1a 2b 3d 4a 5b 6b 7b 8d 9b 10a 11c 12a 13d 14b 15d 16d 17b 18c 19b 20d 21b 22b 23a 24c 25a 26a 27d 28d 29d 30a 31d 32c 33c 34a 35a 36c 37a 38a 39a 40d

  

RATIO & PROPORTION 

EXERCISE - A

1) If 7A= 5B= 2C; find A: B: C .

a) 35: 40 :10 b) 14 :10 :35 c) 2:5 :7 d) 10: 14:35 

2) If a: b = 3:8, find the value of (5a - 3b)/(2 a + b).

a)  9/14 b) 14/9  c) - 9/14  d) - 14/9

3) If  A:B:C =1:3:5, what is the value of (4A - B + 2C)/3(A + B + C)?

a) 8/27 b) 10/27  c) 11/27 d) 1/3

4)  P/Q =R/S =T/U = 3/4,  then what is the value of (4P+ 5R+7T):(3Q+4S+7U)?

a) 12:19 b) 6:7 c) 3:4 d) 5:8

5) If 25% of X is equals to 40% of Y, then what is the ratio of X and Y

a) 8:5 b) 5 :3 c) 9:5 d) 4:5

6) If 35% of A is equals to 60% of B, the then what is the ratio of A and B?

a)  8:13 b) 12 :7  c) 2:3 d) 13:7 

7) Marks of two candidates x and y are in the ratio 4:7. If the marks of x is 140, then what will be the marks of y ?

a) 210  b) 180 c) 245 d) 225 

8) The bus fare between two cities is increased in the 5:11. Find the increase in the fare, if the original fare is Rs 275

a) 605  b) 121  c) 330 d) 242 

9) Two numbers are in the ratio 3:4. On increasing each of them by 30, the ratio becomes the 9 :10. The numbers are 

a) 30, 40 b) 15, 20 c) 12 ,16 d) 18, 24

10) Two numbers are in the ratio 7:5, On diminishing each of them by 40, the ratio becomes 27:17. The difference between the numbers is?

a) 75  b) 40 c) 25 d) 50 

11) The ratio 2 numbers is 2:3. If the sum of both the numbers is 75, then what is the larger number among both the numbers?

a) 45 b) 30 c) 50 d) 48

12) The ratio of three numbers is 3:6:8. If their product is 9216, then what is the sum of the three numbers?

a) 96 b) 72 c) 144 d) 68 

13) The ratio two numbers is 5:6. If their product is 1470, then what is the sum of both the numbers?

a) 210 b) 77 c) 132 d) 98

14) Of three positive numbers ,nthe ratio first and second is 5:2, ratio of second and third is 5:4, The product of first and third is 1800. What is the sum of the three numbers?

a) 43 b) 133 c) 119  d) 129 

15) The sum of the three numbers is 162. If the ratio of the first number to the second number is 5:7 and that of the second number to the third number is 5:3, then what is the second number ?

a) 35 b) 70 c) 80 d)  40 

16) 3 numbers are in the ratio 1/2: 2/3 :3/4. The difference between the greatest and the smallest number is 27. The average of three numbers is 

a) 40 b) 81 c) 69  d) 54 

17) If Simran's salary is 7/6 times of Owais and Khushi 's is 8/7 times of Owais, what is the ratio of Simran's salary to Khushi?

a) 49:48 b) 3:4 c) 4:3 d) 48:49

18) In any army selection process, the ratio of selected to unselected candidates was 9 : 2. If 80 less had applied and 20 lessnselected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process ?

a) 6160 b) 1540 c) 3080 d):9240 

19) In an examination, the success to failure ratio was 5:2. Had the number of failure been 14 more, then the success to failure ratio would have been 9:5. The total number of candidates who appeared for the examination was 

a) 210  b) 196 c):126 d) 203

20) x and y are two numbers such that their mean proportion is 16 and third proportion is 128. What is the value of x and y ?

a) 8 and 16 b) 16 and 32 c) 8 and 32 d) 16 and 16 

21) What is the ratio between the fourth proportion of 3, 4, 9 and the mean proportional between 2 and 98 ?

a) 7:8 b) 7:6 c) 8:7  d) 6:7 

22) Rs18200 is divided among X,Y, Z in the ratio 1/3 , 1/4 :1/2. What is the share in rupees of X?

a)  7000 b) 4400 c);4250 d):5600

23) Rs7750 is divided among X,y,z such that 3 times of X's share is equal to 5 times of y's share which is equal to 2 times of z's share . What is the share (in Rs) of z?

a) 4250  b) 3750 c) 3875 d) 4475

1d 2c 3c 4b 5a 6b 7c 8c 9b 10d 11a 12d 13b 14d 15b 16c 17a 18c 19b 20c 21d 22d 23b 

EXERCISE - B

1) Rs6300 is divided between x, y, z such that x: y= 7:5 and y: z =4:3. Find the share of y.

a) 1800  b) 2000 c) 2200 d) 2400

2) What is the ratio of the mean proportional between 14.4 and 3.6 then the third proportional the third proportional of 5 and 4 ?

a) 4: 9 b) 5:8 c) 9:4 d) 8:5

3)  Two numbers A and B are in the ratio 5:2. If 4 is added to each number, then this ratio becomes 9:4. If 5 is subtracted from each of the original numbers , then the ratio of A and B will be?

a) 3:1 b) 8: 3 c) 7:2  d) 4:1 

4) Three numbers are in the ratio 1/2: 2/3: 3/4. The difference between the greatest and the smallest number is 27. The smallest number is 

a) 81 b) 40 c) 72  d) 54 

5) Incomes of A and B are in the ratio 5:3 and their expenditures are in the ratio 9:5. If income of A is twice the expenditure of B, then what is the ratio of savings of A and B?

a) 2:3  b) 1: 1 c) 3:2  d) 3:4 

6) Two numbers are in the ratio of 7:5. On diminishing each of them by 40, the ratio becomes 27: 17. The sum of the numbers is 

a) 300 b) 240 c) 325  d) 275 

7) The ratio of the income of a and b is 2:3 and that of their expenditures is 1:3. If 905 B's expenditure is equal to the income of a,  then what is the ratio of the savings of a  and b ?

a) 1:1 b) 9:8 c) 8:7  d) 3:2 

8) A sum of Rs4360 was to be divided into among A, B, C and D in the ratio of 3:4:5:8,  but it was divided in the ratio 1/3 :1/4 :1/5 :1/8 by mistake, As a result

a) A received Rs956 more

b) B received Rs 318 more

c) D received Rs1144 less

d) C received Rs132 less

9) A crate of eggs holds one rotten eggs out of every 25 eggs in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate, then calculate the number of eggs in the crate .

a) 380  b) 400 c) 420 d) 440

10) The ratio of 2 numbers is 6:11 and their difference is 65. What will be the smaller number among both the numbers ?

a) 58 b) 65 c) 52 d) 78 

11) The ratio of two numbers is 3:7. If their product is 1344, then what is the sum of both the numbers ?

a) 80 b) 60 c) 30 d) 168

12) If the ratio of two numbers is 5:4, if the sum of both the numbers is 180, then what is the larger number among both the numbers ?

a) 100 b) 80 c) 60 d) 75

13) The ratio 3 numbers is 2:3:5. If the sum of the 3 number is 275, then what is the largest among three numbers ?

a) 142 b) 82.5  c) 137.5 d) 152

14) The ratio of 3 numbers is 5:6:8 if the sum of the three number is 380,  then what is the smallest among the three numbers ?

a) 75 b) 80 c) 120 d) 100

15) The sum of three numbers is 67. If the ratio of the first number to the second number is 3:5 and that of the second number to the third number is 4:7, then what is the second number?

a)  20 b) 24 c) 18 d) 16 

16) A sum of the Rs3170 is divided among x, y, z such that if Rs13 , Rs12 and Rs18 will be diminished from the shares of x, y and z respectively, then their share will be in the ratio 20:18 :21. What is the initial share (in Rs) of z?

a) 1131 b) 1530 c) 910 d) 1350

17) if a: b=7 :9 and b: c= 15:7 then a: c =

a) 5:3 b) 7 :21  c) 3:5 d) 7 :15

18) (3A + 5B)/(3A - 5B) = 5, then a:b = ?

a) 2: 1 b) 5:3 c) 3 :2 d) 5:2 

19) calculate the third proportional to 16 and 32?

a) 16 b) 32 c) 64 d) 132 

20) if a, b, c ,d and e are in continued proportion, then a/e is equals to 

a) a³/b³ b) a⁴/b⁴ c) b³/a³ d) b⁴/a⁴

21) Find the 4th proportional to 3, 7 and 9.

a) 21 b) 22 c) 10 d) 8 

22) The fourth proportional to p²- pq +q², p³+ q³, p - q is

a) p+ q b) p - q c) p²+ q² d) p² - q²

23) What is the mean proportional between (15 + √200) and (27- √648) ?

a) 4 b) 14√7 c) 3√5 d) 5√3 

24) Find the value of (a + b)/(a -b), if  a/b= 5/3

a) 2/3 b) 8/5 c) 5/8 d) 4

1b 2c 3a 4d 5b 6a 7a 8c 9b 10d 11a 12a 13c 14d 15a 16a 17a 18d 19c 20b 21a 22d 23c 24a 

EXERCISE - C

1) If A: B=3:4 and B: C= 6:7, find:

a) A: C.

b) A: B: C.

2) If P: Q=9:4 and P:R= 6:11, find:

a) Q: R.

b) P: Q: R

3) Share out 120 hours of computer time between 4 scientists in the ratio 2:1:4:3.

4) The population of three villages are 2500, 3750 and 7500. A consignment of 13200 tonnes of grain is to be shared according to the population. How much goes to each village ?

5) Increase Rs450 in the ratio 5:2.

6) Decrease 7.20 kg in the ratio 7:11.

7) Divide Rs6902 among A, B and C so that A's share is to B's share as 1:2 and B's share is to be  3:4.

8) Divide 3900 among A, B and C so that the four times A's share, three times B's share and twice C's share may all be equal.

9) Find : i) the four proportion to 6, 7 and 9.

ii) the third proportional to 2.4 and 0.72.

ii) the mean proportional to 8 and 18.

10) Two numbers are in the ratio 5:4. When 30 is subtracted from each, the resulting numbers have the ratio 4:3. Find the numbers.       

11) A garrison of 3000 men has provisions for 64 days. At the end 24 days, reinforcement arrives and it is found that now the remaining provisions will last 24 days only. What is the strength of reinforcement.

12) A man undertakes to do a certain work in 150 days. He employees 200 men. He finds that only a quarter of the work is done in 50 days .  How many additional men should he employ so that the whole work is finished in time ?

13) A garrison of 3600 men was provisions for 15 weeks. How long will the provisions last, if 900 more men join them and the daily allowance per man is reduced by 20%?

14) If 50 men can do a piece of work in 12 days working 8 hours a day, how many hours a day would 60 men have to work in order to do another piece of work, twice as big in 16 days ?

15)  Two men undertakes to do a piece of work for Rs288. One can do it in 8 days and the other in 9 days; but with the help of a boy they finish the work in 7/2 days. Find the share of each in the money.

16) A car travelling at 90 kmph completes a certain journey in 40 minutes. How long would it take a car travelling at 

a) 100 kmph

b) 75 kmph to complete the same journey?

17) Water flows constantly into a cylindrical beaker with a base area 24 cm². The water level rises by 10cm every second. How quickly would the water level rise in a beaker with a base area of

a) 20 cm²

b) 30 cm², if the flow rate remains the same.

18) A 1.2 kilowatt electric heater boils a given amount of water in 10 minutes. How long would it take

a) a less powerful heater of 800 watts.

b) a more powerful heater of 2 kilowatt to boil the same amount of water?

19) A man walks from his house at 5 km an hour and reaches his office 20 minutes late. If his speed had been 15/2 kmph, he would have reached 12 minutes early. How far his office from his house ?

20) A man sitting in a train, which is travelling at the rate of 50 kmph, observes that it takes 6 seconds for a good train, travelling in the opposite direction, to pass him. If the goods train is to 220 m long, its speed.

21) A train overtakes two person who are walking in the same direction at 2 kmph and 4 kmph respectively and passes them in 9 seconds and 10 seconds respectively. Find the length of the train and its speed in kmph .

22) A railway train crosses a platform 110m long in 10 seconds and passes a telegraph post in 5 seconds . Find the length of the train and its speed per hour.

23) A boat moves down 0-steam at the rate of 1 km in 6 minutes and upstream at the rate of 6 kmph. What is the velocity of the current ?

24) The current of a stream runs at the rate of 5 kmph . A motor-boat goes 10 km upstream and back again to its starting point in 50 minutes. Find the speed of the motor boat in still water.

25) Find two numbers in the ratio of 5 to 4 so that the difference of their cubes is 488.

26) A certain number of labourers promise to do a certain piece of work in 10 days, but 5 of them become absent. If the rest of the labourers complete the work in 12 days, find their original number.

27) A man can walk 600 km in 35 days, resting 9 hours each day; how long will he take to walk 375 km if he rests 10 hours each day and walks 3/2 times as fast as before?

28) How many one rupees coins , fifty paise coins and twenty -five paise coins, of which the numbers are proportional to 4, 5 and 6, are together worth Rs96 ?

29) If 3 men or 4 women can reap a field in 43 days; how long will 7 men and 5 women take to reap it ?

30) Two pipes  P and Q can fill a cistern in 12 minutes and 15 minutes respectively. Both are opened together, but at the end of 3 minute the first is turned off . In how much time will the remaining cistern be filled?

31) Two men A and B walk from P to Q (a distance of 21 km) at 3 kmph and 4 kmph respectively. B reaches A, returns immediately and meets A at R. Find the distance from P to R.

32) The wheel of an engine, 4 m 20 cm in circumference, makes 15 revolutions in 4 seconds ; find the speed of the engine in kmph.

EXERCISE - D

1) Two vessel contain milk and water in the ratio 7:5 and 7:9 if both vessel are mixed in the ratio 1:1, find the ratio of milk and water in new mixture ? 49:47

2) Three vessel each of 10 litre capacity contain a mixture of milk and water in the ratio 2:1, 3:1, 3:2. If all the three vessels are emptied in to a large vessel, find the ratio of milk and water in new mixture ?                       121:59

3) 2 vessel A and B contains a mixture of milk and water in the ratio 4:5 and 5:1. If both vessel are mixed in the ratio 5:2. Find the ratio of milk and water in new mixture.                    5:4

4) A 2 kg of metal of which 1/3 is zinc and rest is copper mixed with 3 kg of metal of which 1/4th is zinc and rest is copper. What is the ratio of zinc to Copper in new mixture.             17:43

5) Ratio of land: water on Earth is 1:2 and ratio of land water in Northern hemisphere is 2:3. Find the ratio of land: water in the southern hemisphere.   4:11

6) ₹ 5600 is to be divided among A, B, C, D in such a way that the ratio of share of A: B is 1:2, B:C is 3:1, C:D is 2:3. Find the share of A + B.               ₹3600

6) The ratio of the expenditure of A, B and C 16:12:9 and their total income is ₹1530. Find the share of B's income. If they save 20%, 25% and 40% of their income ?                 ₹480

7) The total income of A, B and C is ₹ 6060. A spend 80%, B spend 85% and C spend 75% and the ratio of their saving is 5:6:9. Find the income of A ?   1500

8) ₹2366 is divided among 8 men, 10 women and 10 children. Each men get 25% more than each women and each woman get 25% more than a child. Find the amount received by each women.   84.5

9) ₹ 500 is divided among A, B, C in such a way that ₹16 more than 2/5 of A's share, ₹ 70 less than 3/4 of B's share , and ₹4 less than 3/5 of C's share are equal. Find B's share.             200

10) A boy and a girl playing with the pencil. The girl break the pencil in two parts and the boy observe that the ratio of the length of these two parts is same as the ratio of length of pencil to the larger part. Find the ratio in which the girl break the pencil.         √5+1:2

11) The ratio of income of A and B is 3:2 and ratio of their expenditure is 4:3. If they save ₹2000 and  ₹900. Find their income.              7200,4800

12) The ratio of total amount distributed in all the male and female as salary is 6:5 while the ratio of salary of each male and each female is 2:3. Find the ratio of number of male and female?       9:5

13) ₹430 is divided among 45 persons such that the ratio of total amount received by all men, all women and all childrens are in the ratio 12:15:16. While the ratio of the amount received by each men, each women and each child is 6:5:4. Calculate the number of men, women and children and also find the amount received by each of them.   12, 10

14) ₹5625 is divided among A,B and C in such a way that A receive 1/2 the sum of B + C . Find the amount received by A+ B . If B received 1/4th of A+ C .        3000

15) The ratio of last year income of A, B, C is 3:4:5. While the ratio of their last year income to current year income 4:5, 2:3 and 3:4. If their total current year income is ₹98500. Find the present income of B+C .          ₹76000

16) 1 year ago the ratio of income of A and B is 3:5. The ratio of their Last year income to current year income is 2:3 and 45. If their total current year income is ₹4300. Find their present income indivisually ?           1800,2500

17) Ratio of income of A,B,C is 3:7:4 and the ratio of their expenditure is 4:3:5. If A saves 100/7% of his income. Find the ratio of their saving.            6:71:11

18) A dog chase a rabbit. The dog takes 6 leaps for every 7 leaps of the rabbit and the distance covered by rabbit in 6 leaps is equal to the distance covered by dog in 5 leaps. Find the ratio of their speed.         36:35

19) The dog takes 7 jumps for every 10 jumps of the Lion And a Fox takes 12 Jumps for every 10 jumps of the lion. And the distance covered by dog in five Jumps , distance covered by lion in 15 jumps and the distance covered by Fox in 20 jumps is equal. Find the ratio of their speeds .            84:40:36

20) The price of gold is directly proportional to square of its weight. A person broke down the gold in the ratio of 3:2:1 and sold, incurrs a loss of ₹4620. Find the initial price of gold.    ₹7560

21) A is inversely proportional to the cube of B. if A=3 then B=2 But if A=8/9 then B=?               3

22) A bag contain 1₹, 50p and 25p coins and the ratio of number of coins is 5:7:9. If the total value of all coins is ₹430. Then find the number of 50p coins.  280

23) A bag contains 1₹, 50p and 25p coins and the ratio of their value is 30 :11 :7. and the total number of coins are 480. Find the number of 50p coins.    132

24) Find the mean proportion of 1/4 and 1/9.                 1/6

25) Find the 3rd proportion 18, 36.   72

26) Find the fourth proportion of 12, 16, 18.   24

27) ₹ 710 is divided among A, B, C in such a way that A receives ₹40 more than B, C receives ₹30 more than A . Find the share of A .               ₹240

28) The ratio of the age of Ram and Shyam 5 years ago was 2:3 and the ratio of their ages after 5 years would be 3:4. Find the sum of their present ages.  60

29) The ratio of the ages of Ram and Shyam 5 years ago was 3:1 and the ratio of their age after 5 years will be 2:1. Find the present age of both.           35,15

30) The age of Ram is 4 times of his daughter. The age of Ram was 9 times of her daughter 5 years ago. Find their present ages.           32, 8

31) The age of father is three times of his son. 5 years before the age of Son was 1/6 time of his father. Find the present age of son. At the time of marriage of his mother, she was 5 years younger to his father. Find the age of mother.           20

32) The ratio of the age of Meena and her mother is 3:8. Find the ratio of their ages after 4 years. If after 10 years their age difference will be 35 years.       5:12

PERCENTAGE 

1) If A= 400 and B = 600, then A is how much percentage less than B?

a) 66.66 b) 25 c) 33.33 d) 50 

2) if C= 1200 and D =1500 then D is how much percentage more than C?

a) 20 b) 33.33 c) 25  d) 125

3) A period of 4 hour and 30 minute is what percentage of a day?

a) 75/4 b) 20 c) 50/3 d) 19

4) when a number is increased by 28, it becomes 107% of itself. What is the number?

a) 336  b) 420 c) 400 d) 252

5) two numbers are 35% and 50% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number ?

a) 23.80 b) 15  c) 25 d) 30

6) if the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35. What is the original fraction?

a) 3/10 b) 2/15 c) 3/14 d) 2/7 

7) Shudha spends 80% of her income when her income is increased by 30%. She increases her expenditure by 25%. Her savings are

a) increased by 5%  b) decreased by 30% c) decreased by 5%  d) increased by 5%

8) The price of commodity is increased by 36% at the quantity purchased is decreased by 30%. What is the percentage increase or decrease in the amount spent on the commodity ?

a) 3.6% increase b) 4.8% increase c) 6% decrease d) 4.8% decrease 

9) A number is decrease by 30% then increased by 30%, then further decreased by 10%. What is the net increase/decrease percent in the number (correct to the nearest integer)?

a) 18% increase b) 19% decrease c) 19% increase d) 18% decrease 

10) Sudha decided to donate 12% of her monthly income to an orphanage . On the day of donation, she changed her decision and donated a sum of Rs4800 which was equals to 80% of what she had decided earlier. what is 27% of her monthly income?

a) 13959 b) 11934 c) 14040 d) 13500

11) A student multiplied a number by 4/7 instead of 7/4. What is the percentage error in the calculation ?

a) 206.25 b) 67.35 c) 33.67 d) 103.13

12) A candidate scores 20% and fails by 50 marks, while another candidate who scored 40% marks, get 30 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination.

a) 500  b) 450 c) 300 d) 400

13) For an examination of a practical based subject, the total marks is 100. The break-up for theory, practical project and viva voce is 40%, 30%, 20% and 10% respectively. A candidate scored 80% in theory, 70% in practical, 60% in project and 50% in viva voce. What was her aggregate percentage ?

a) 70 b) 72  c) 68 d) 67 

14) Two students appeared for an examination. One of them secured 21 marks more than the other and his marks were 80% of the sum of their marks. The marks obtained by them are

a) 88 and 67 b) 89 and 68 c) 28 and 7 d) 98 and 77 

15) Two students appeared for an examination. One of them secured 13 marks more than the other and his marks were 76% of the sum of their marks. The marks obtained by them are 

a) 19 and 6 b) 34 and 21 c) 102 and 89 d) 92 and 79 

16) The price of petrol is increased by 24%. A percent wants to increase his expenditure by 14% only. By what percentage (correct to one decimal place) should he decrease his consumption in order to maintain the same level of Expenditure?

a) 8.3 b) 7.9 c) 8.1 d) 7.8 

17) The price of sugar got raised by 25%. To maintain the same level of expenses on sugar, a person reduced the consumption of sugar by 4% and also increased his expenditure on Sugar by x%. The value of x is 

a) 19.5%  b) 21% c) 20%  d) 18.75%

18) The price of an article increases by 20% every year. If the difference between the prices at the end of the third and fourth year is Rs259.20, then 40% of the price( in Rupees) at the end of second year is 

a) 484 b) 432 c) 384 d) 472 

19) Two students A and B appeared for an examination. A secured 8 marks less than B and the marks of the former was 60% of the sum of their marks. The sum of the marks obtained by A and B is 

a) 45  b) 50 c) 40 d) 75 

20) The sum of the salaries of A and B is Rs42000. A spends 75% of his salary and B spends 90% of his salary. Now their savings are the same. What is A's salary(in Rs)?

a) 18000 b) 12000 c) 30000 d) 15000

21) The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and  25% the girls are scholarship holders, then the percentage of students, who do not get the scholarship, is

a) 78 b) 75 c) 60 d) 55 

22) The sum of the salaries of A and B together is Rs43000. A spends 95% of his salary and B , 80% of his salary. If now their are savings are the same. What is B's salary?

a) 8000 b) 34400 c) 10600 d) 8600 

23) Sohan spends 23% of an amount of money on an insurance policy, 33% on food , 19% on children's education and 16% on recreation. He deposits the remaining amount of Rs504 in bank. How much total amount does he spend on food and insurance policy together ?

a) 3200 b) 3126 c) 3136  d) 3048

24) With reference to a number greater than one, the difference between itself and its reciprocal is 25% of the sum of itself and its reciprocal. By how much percent (correct one decimal) is the fourth power of the number greater than its square?

a) 57.8 b) 62.5 c) 64.5 d) 66.7 

25) For a number, greater than one, the difference between itself and its reciprocal is 20% of the sum of itself and its reciprocal. By how much percentage (nearest to one integer) is the square of the number less than its cube ?

a) 122 b) 18 c) 81 d) 33 

26) The population of a town increases by 5% in the first year, by 6% in the second year and 8% in third year. The present population of town is 120204. What you was the population of town in 3 years ago ?

a) 102000 b) 100000 c) 98000 d) 101204

27) In an examination, 20% of total number of students failed in History . 15% of total number of students failed in Hindi and 5% of total number of students failed in both. Find the percentage of students who passed in both the subjects.

a) 50 b) 60 c) 70 d) 80

28) In 2019, ratio of number of students who taking part in examinations x, y and z States is respectively 3 : 5 : 6. Next year, the number of students are increased by 20%, 10% and 20% respectively. If ratio of the number of students in States x and z is 1:2, find the number of students who sit to take part in 2019 

a) 5000 b) 6000 c) 75000 d) data inadequate

29) In a constituency, 40% of the voters are senior citizens. 40%  of the senior citizen voters are illiterates and 25% of the non-senior citizen voters are literates. By what percentage is the number of literate senior citizens voters less than that of illiterate non-senior citizen voters?

a) 40 b) 145/3 c) 50 d) 140/3

1c 2c 3a 4c 5d 6c 7d 8d 9d 10d 11b 12d 13a 14c 15a 16c 17c 18b 19c 20b 21a 22d 23c 24d 25b 26b 27c 28d 29d 

EXERCISE - B

1) Kavita attendance in her school for academic session 2018- 2019 was 216 days. On computing her attendance, it was observed that are attendance was 90%. The total working days of the school were

a) 194 b) 250 c) 240 d) 195 

2) If x% of y is150 and y% of z is 300, then the relation between x and z is 

a) z= x b) z= x/3 c) z= x/2 d) z==2x

3) A is 20% more than B, B is 25% more than C, C is 60% less than D and D is 20% more than E. Based on the above information, which of the following is true ?

a) D is 60% less than B

b)  E is 28% more than A

c) A is 40% less than D

d) C is 24% less than A 

4) Anu spent 90% of her income. If her expenditure increases by 25% and savings increases by 30%, then by what percent does her salary increase ?

a) 25.5%  b) 24% c) 22.5% d) 20% 

5) A number is decreased by 30%, then increased by 30%, then further increased by 30%. What is the net increase/decrease percent in the number (correct to the nearest integer)?

a) 18% increase  b) 18% decrease c) 19% decrease d) 19% increase 

6) A man spends 72% of his income. If his income increases by 28% and his expenditure increases by 25%, then what is the percentage increase or decrease in his savings (incorrect to one decimal places)?

a) 26.9% decreases b) 38.4% increase c) 35.7% increase d) 26.3% decrease 

7) The sum of the salaries of A and B is Rs42000. A spends 75% of his salary and B spends 90% of his salary. Now their savings are the same. What is B' s salary 

a) 18000  b) 12600 c) 15000 d) 30000

8) Two students, A and B appeared for an examination. A secured 8 marks more than B and the marks of the former was 55% of the sum of their marks. The sum of the marks obtained by A and B is 

a) 100 b) 80 c) 75  d) 90 

9) 90% of x= 40% of y and y=  a% of x. What is the value of a?

a) 225 b) 125 c) 2.25 d) 1.25

10) If R= 97 and S= 1552, then S is how much percentage more than R ?

a) 60 b) 37.5 c) 58.2 d) 48 

11) Rahul's salaries is 40% of Mohit's salary. If Rahul 's salary is increased by 60% and Mohit's salary is decreased by 20%, then Rahul's salary will be how much percentage of Mohit's salary ?

a)  80 b) 100 c) 106 d) 64

12) 29 is 0.8% of

a) 3625 b) 1450 c) 7250 d) 10875

13) If 35% of (x+ y)= 40% of (x - y), then x is what percent of y?

a) 1500 b) 150 c) 15 d) 105 

14) if x = 600 and y = 800, then x is how much percentage less than y?

a) 33.33 b) 25 c) 75 d) 35

15)  The price of an article is cut by 3%. To restore its original value, the new price must be increased by 

a) 3% b) 7.11% c) 3.09% d) 2.69%

16) On decreasing the price of a fan by 40%, Its sales increases by 50%. What will be the percentage increasees or decreases in its revenue?

a) 15% increase b) 15% decrease c) 10% decrease d) 10% increase

17) If in the population of a town there is n increase of 44% in first year and 75% in the second year, then what is the average rate of increase in the population ?

a) 45% b) 59.5%  c) 74% d) 76% 

18) A student multiplied a number by 5/7 instead of 7/5. What is the percentage error in the calculation ?

a) 48.98% b) 96% c) 24.49% d) 48%

19) Price of 1 kg of sugar is increased by 30% and the increase is Rs48. What is the new price( in Rs) of the sugar per kg?

a) 178 b) 160 c) 208 d) 2016

20) The sum of the salaries of A and B together is Rs45000. A spend 85% of his salary and B, 70% of his salary . Now their savings are the same. What is B's salary

a)  30000 b)  18000 c) 12600 d) 15000

1c 2d 3c 4a 5a 6c 7d 8b 9a 10a 11a 12a 13a 14b 15c 16c 17d 18a 19c 20d 

SAP- C

1) A sells his goods 30% cheaper than B and 30% dearer than C. By what percentage is the cost of C's good cheaper than B's goods.        46.15%

2) The length and the breadth of a rectangle are changed by +20% and by -10% respectively. What is the percentage change in the area of the rectangle .     8%

3) Due to a 25% price hike in the price of rice. A person is able to purchase 20kg less rice for Rs 400. Find the initial price.     

4) A's salary is 20% lower than B's salary, which is 15% lower than C's salary. By how much percentage is C's salary more than A's salary?      3200/68

5) The cost of manufacture of an article is made up of a components A, B, C, D which have a ratio of 3:4:5:6 respectively . If there are respective changes in the cost of +10%, +20%, -30% and +40%, then what would be the percentage change in the cost.     2.22%

6) Harsh receives an inheritance of a certain amount from his grandfather. Of this he loses 32.5% in his effort to produce a film. From the balance, a taxi driver stole the sum of 100000 that he used to keep in his pocket. If the rest, he donated 20% to a charity. Further he purchases a flat in Ganga Apartment for Rs 7.5 lakh. He then realizes that he is left with only 2.5 lakh cash of his inheritance. What is the value of his inheritance.      2.5 lakh

SAP- D

1) Which of the following is the largest number ?

a)  20% of 200 b) 7% of 500  c) 1300% of 3 d) 600% of 7 

2) if 25% of a number is 75, then 45% of the number is 

a) 145  b) 125 c) 150 d)  135 

3) What is 20% of 50% of 75% of 70 .

a) 5.25 b) 6.75 c) 7.25  d) 5.25

4) if we express 41(3/17)% as a fraction, then it is equals to 

a) 17/7  b) 7/17 c) 12/17 d) 3/17

5) Mr. Abhimanyu Banerjee is worried about the balance of his annual monthly budget. The price of petrol has an increased by 40%. By what percent should he reduce the consumption of petril so that he is able to balance his budget

a) 33.33 b) 28.56  c) 25  d) none 

6) In question 5, if Mr. Banerjee wanted to limit the increase in his expenditure to 5% on his basic expenditure on petrol then what should be the corresponding decrease in consumption so that expenditure exceeds only by 5% ?

a) 33.33 b) 28.56 c) 25 d) none 

7) Ram sells his goods 25% cheaper than shyam and 25% dearer than Bram. How much percentage is Bram's goods cheaper than Shyam's ?

a) 33.33% b) 50% c) 66.66% d) 40%

8) In an election between two candidates , Bhiku gets 65% of the total valid votes. If the total votes were 6000, what is the number of valid votes that the other candidate Mhatre gets if 25% of the total votes were declared invalid?

a) 1625 b) 1575 c) 1675 d) 1525

9) In a medical certificate, by mistake a candidate gave his height as 25% more than the normal. In the interview panel, he clerified that his height was 5feet 5 inches. Find the percentage correction made by the candidate from his stated height to his actual height.

a) 20 b) 28.56 c) 25 d) none 

10) Arjun Sharma generally wears his father's coat. Unfortunately, his causin Shaurya poked him one day that he was wearing a coat of length more than his height by 15%. If the length of Arijit 's father's coat is 120cm then find the actual length of his coat .

a) 105 b) 108 c) 104.34 d) 102.72

11)  A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due to this mistake

a) 96% b) 95%  c) 2400% d) none

12) Harsh wanted to subtracte 5 from a number. Unfortunately, he added 5 instead of substracting. Find the percentage change in the result.

a) 300% b) 66.66% c) 50% d) cannot determined

13) If 65% of x= 13% of y, then find the value of x if y= 2000.

a) 200 b) 300 c) 400 d) 500

14) In a mixture of 80 litres of milk and water, 25% of the mixture is milk. How much water should be added to the mixture so that milk becomes 20% of the mixture?

a) 20 b) 15 c) 24 d) none 

15) 50% of a% of b is 75% of b% of c. Which of the following is c?

a) 1.4a b) 0.667a c) 0.4a d) 1.25a

16) A landowner increased the length and the breadth of a rectangular plot by 10% and 20% respectively. Find the percentage change in the cost of the plot assuming land prices are uniform throughout his plot.

a) 33% b) 35% c) 22.22% d) none 

17) The height of a triangle is increased by 40%. What can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60%

a) 50% b) 20% c) 14.28% d) 25%

18) The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

a) 77% b) 75% c) 88% d) 98%

19) The salary of Amit is 30% more than that of Varun. Find by what percentage is the salary of Varun less than of Amit ?

a) 26.12% b) 23.07% c) 21.23% d) none 

20) The price of sugar is reduced by 25% but inspite of the decrease, Ayush ends up increasing his expenditure on sugar by 20%. What is the percentage change in his monthly consumption of sugar?

a) +60% b) -10% c) +33.33% d) 50%

21) The prize of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20kg of rice previously?

a) 5kg b) 15kg c) 25kg d) 30kg

22) 30% of a number when subtracted from 91, gives the number itself. Find the number 

a) 60 b) 65 c) 70 d) none 

23) When 60% of a number A is added to another number B, B becomes 175% of it's previous value. Then which of the following is true regarding the values of A and B?

a) A> B b) B > A c) Either can be true depending upon the values of A and B 

d) nothing can be said 

24) At an election the candidate who got 56% of the votes cast won by 144 votes. Find the total voters on the voting list if 80% people cast their vote and there were no invalid votes.

a) 360 b) 720 c) 1800 d) 1500

25) The population of a village is 100000. The rate of increase is 10% per annum. Find the population at the start of the third year?

a) 133100 b) 121000 c) 120000 d) none 

26) The population of the village of Gavas is 10000 at this moment. It increases by 10% in the first year. However, in the second year, due to immigration, the population drops by 5%. Find the population at the end of the third year if in the third year the population increases by 20%.

a) 12340 b) 12540 c) 127540 d) 12340

27) A man invests Rs 10000 in some shares in the ratio 2:3:5 which pay dividends of 10%, 25% and 20%(on his investment) for that year respectively. Find his dividend income.

a) 1900 b) 2000 c) 2050 d) 1950

28) In an examination, Mohit obtained 20% more than Sushant but 10% less than Rajesh. If the marks obtained by Sus is 1080, find the percentage marks obtained by Rajesh if the full marks is 2000.

a) 86.66% b) 72 % c) 78.33% d) none

29) In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (counting the final scores of the candidates).

a) 37.266 b) 37.6 c) 37.8 d) 36.93

30) Ram spends 20% of his monthly income on his household expenditure, 15% of the rest on books, 30% of the rest on clothes and saves the rest. On counting, he comes to know that he has finally saved Rs 9520. Find his monthly income.

a) 10000 b) 15000 c) 20000 d) none 

31) Hans and Bhaskar have salaries that jointly amount to Rs 10000 per month. They spend the same amount monthly and then it is found that the ratio of their savings is 6:1. Which of the following is Han's salary?

a) 6000 b) 5000 c) 4000 ds) 3000

32) The population of a village is 5500. If the number of males increases by 11% and the number of females increases by 20%, then the population becomes 6330. Find the population of females in the town.

a) 2500 b) 3000 c) 2000 d) 3500

33) Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percentage is Vicky's salary more than Ashu's?

a) 96% b) 51.1% c) 90% d) 51.1%

34) In a shelf, the first row contains 25% more books than the second row and the third row contains 25% less books than the second row. If the total number of books contained in all the rows is 600, then find the number of books in the first row.

a) 250 b) 225 c) 300 d) none 

35) An ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. How many kilograms of the ore are needed to obtain 60 kg pure iron?

a) 250 b) 275 c) 300 d) 266.66

36) Last year, the Indian cricket team played 40 oneday cricket matches out of which they managed to win only 40%. This year, so far it has played some matches, which has made it mandatory for it to win 80% of the remaining matches to maintain its existing winning percentage. Find the number of matches played by India so far this year?

a) 30 b) 25 c) 28 d) Insufficient Information 

37) The population of a village is 100000. Increase rate per annum is 10%. Find the population at the starting of the fourth year 

a) 133100 b) 121000 c) 13300 d) none 

38) In the recent climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian?

a) 73% b) 77% c) 79% d) 83%

39) A cow and a calf cost Rs 2000 and Rs 1400 respectively. If the piece of the cow and that of the calf is increased by 20% and 30% respectively then the price of 1 dozen cows and 2 dozens calves is 

a) 72480 b) 71360 c) 74340 d) none 

40) Ram sells his goods 20% cheaper than Bobby and 20% dearer than Chandilya. How much percentage is Chandilya's goods cheaper than Bobby's 

a) 33.33% b) 50% c) 42.85% d) none

41) During winters, an athlete can run x metres on one bottle of glucose. But in the summer, he can only run 0.5x metres on one bottle of glucose. How many bottles of glucose are required to run 400 metres during summer?

a) 800/x b) 890/x c) 96 d) 454/x

42) Out of the total production of iron from hematite, an ore of iron, 20% of the ore gets wasted, and out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80000 kg, then the quantity of hematite mined from that mine in the year is

a)  500000 kg b) 400000 kg c) 450000 kg d) none 

43) A man buys a truck for Rs 250000. The annual repair cost comes to 2.0% of the price of purchase. Besides, he has to pay an annual tax of Rs 2000. At what monthly rent must he rent out the truck to get a return of 15% on his annual investment?

a) Rs 3350 b) Rs 2500 c) Rs 4000 d) Rs 3212.50

44) Recently, while shopping in Patna Market in Bihar, I came across two new shirts selling at a discount. I decided to buy one of them for my little boy Sherry. The shopkeeper offered me the first shirt for Rs 42 and said that it usually sold for 8/7 of that price. He then offered me the other shirt for Rs 36 and said that it usually sold for 7/6 th of that price. Of the two shirts which one do you think is a better bargain and what is the percentage discount on it?

a) first shirt, 12.5% b) second shirt, 14.28% c) both are same d) none 

45) 4/5th of the voters in Bellary promised to vote for Sonia Gandhi and the rest promised to vote for Sushma Swaraj. Of these voters, 10% of the voters who had promised to vote for Sonia Gandhi, didn't vote on the election day, while 20% of the voters who had promised to vote for Sushma Swaraj did not vote on the election day. What is the total number of votes polled if Sonia Gandhi gpt 216 votes?

a) 200 b) 300 c) 264 d) 100

46) In an examination, 80% students passed in Physics, 70% in chemistry while 15% failed in both the subjects. If 325 students passed in both the subjects. Find the total number of students who appeared in the examination.

a) 500 b) 400 c) 300 d) 600

47) Ravana spends 30% of his salary on his rent, 30% of the rest he spends on his children's education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs 2500. What is Ravana's salary?

a) Rs 11494.25 b) Rs 20000 c) Rs 10000 d) Rs 15000

48) The entrance ticket at the Minerva theatre in Mumbai is worth Rs 250. When the price of the ticket was lowered, the sale of tickets increased by 50% while the collections recorded a decrease of 17.5%. Find the deduction in the ticket price.

a) Rs 150 b) Rs 112.5 c) Rs105 d) Rs 120

48) Ravi's monthly salary is A rupees. Of this, he spends X rupees. The next month he has an increase of C% in his salary and D% in his expenditure. The new amount saved is:

a) A(1+ C/100) - X(1+ D/100)

b) A/100(C - (D)X(1+ D/100)

c) X(C - (D)/100

d) X(C + (D)/100

50) In the year 2000, the luxury car industry had two car manufacturers -- Maruti and Honda with market shares of 25% and 75% respectively. In 2001, the overall market for the product increased by 50% and a new player BMW also entered the market and captured 15% of the market share. If we know that the market share of Maruti increased to 50% in the second year, the share of Honda in that year was:

a) 50% b) 45% c) 40% d) 35%

1d 2d 3a 4b 5b 6c 7d 8b 9a 10c 11c 12d 13c 14a 15b 16d 17c 18d 19b 20a 21c 22c 23a 24d 25b 26b 27d 28b 29b 30c 31a 32a 33a 34a 35d 36d 37a 38c 39a 40a 41a 42b 43d 44b 45c 46a 47c 48b 49a 50d

SAP- E

1) Bill Ambani, a very clever businessman, started off a business with very little capital. In the first year, he earned a profit of 50% and donated 50% of the total capital (initial capital+ profit) to a charitable organisation. The same course was followed in the 2nd and 3rd years also. If at the end of three years, he is left with Rs 16875, then find the amount donated by him at the end of 2nd year 

a) 45000 b) 12500 c) 22500 d) none 

2) In an examination, 48% students failed in Hindi and 32% students in History, 20% students failed in both the subjects. If the number of students who passed the examination was 880, how many students participated in the examination if the examination consisted only of these two subjects?

a) 2000 b) 2200 x) 2500 d) none

3) At IIM, Lucknow, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a few waiver. If the number of those getting a few waiver is 90, find the total number of students getting 50% concession if it is given that 50% of those not getting a few waiver are eligible to get half fee concession?

a) 360 b) 280 c) 320 d) 330

4) A machine depreciates in value each year at the rate of 10% of its previous value. However, every second year there is some maintenance work so that in that particular year, depreciation is only 5% of its previous value. If at the end of the fourth year, the value of the machine stands at Rs 146204, then find the value of machine at the start of the first year.

a) 190000 b) 200000 c) 195000 d) 210000

5) Arushi 's project report consists of 25 pages each of 60 lines with 75 characters on each line. In case the number of lines is reduced to 55 but the number of characters is increased to 90 per lines, what is the percentage change in the number of pages. (Assume the number of pages to be a whole number).

a) +10% b) +5% c) -8% d) -10%

6) The pri of soap is collectively decided by five factors, research, raw materials, labour, advertisements and transportation. Assume that the functional relationship is:

Price of soap= (k x Research costs x Raw material costs x labour costs x Advertising cost x Transportation cost)

If there are respective changes of 10%, 20%, - 20%, 25% and 50% in the five factors, then find the change in the price of soap.

a) 97% b) 95% c) 98% d) cannot determined

7) After receiving two successive raises, Harsh's salary became equal to 15/8 times of his initial salary. By how much percentage was the salary raised the first time if the second raise was twice as high (in percent) as the first?

a) 15% b) 20% c) 25% d) 30%

8) The ratio of Jim's salary for October to his salary for November was 1.5: 1333 and the ratio of the salary for November to that for December was 2: 2666. The worker got 40 rupees more for December than for October and received a bonus constituting 40 percent of the salary for three months. Find the bonus. (Assume that the number of workdays is the same in every month)

a) 368.888 rupees b) 152.5555 rupees c) 256.6 rupees d) none 

9) After three successive equal percentage rise in the salary the sum of 100 rupees turned into 140 rupees and 49 paise. Find the percentage rise in the salary.

a) 12% b) 22% c) 66% d) 82%

10) Prema goes a shop to buy a sofa set costing Rs 13080. The rate of sales tax is 9%. She tells the shopkeeper to reduce the price of the sofa set to such an extent that she has to pay Rs 13080 inclusive of sales tax. Find the percentage reduction needed in the price of the sofa set to just satisfy her requirement.

a) 8.33% b) 8.26% c) 9% d) 8.5%

11) The price of a certain article was raised by 10% in India. The consumption of the same article was increased from 200 tons to 225 tons. By how much percentage will the expenditure on the article rise in the Indian economy?

a) 24.25% b) 22.5% c) 23.75% d) none 

12) In the university examination last year, Rajesh scored 65% in English and 82% in history. What is the minimum percent he sh score in Sociology, which is out of 50 marks (if English and history were for 100 marks each), if hw aims at getting 78% overall?

a) 94% b) 92% c) 98% d) 96%

13) King Dasaratha, at his eleventh hour, called his three queens and distributed his gold in the following way:

He gave 50% of his wealth to his first wife, 50% of the rest to his second wife and again 50% of the rest to his third wife. If their combined share is worth 130900 kilograms of gold, find the quantity of gold King Dasaratha was having initially?

a) 150000 kg b) 149600 kg c) 151600 kg d) none 

14) The population of New Foundland increases with a uniform rate of 8% per annum, but due to immigration, there is a further increase of population of 1% (however, this 1% increase in population is to be calculated on the population after the 8% increase and not on the previous years population). Find what will be the percentage increase in population after 2 years.

a) 18984 b) 18081 c) 18.24 d) 17.91

15) 10% of Mexico's population migrated to South Asia, 10% of the remaining migrated to America and 10% of the rest migrated to Australia. If the female population, which was left in Mexico, remained only 354500. Find the population of Mexico City before the migration and its effects if it is given that before the migration the female population was half the male population and this ratio did not change after the migration?

a) 1000000 b) 1200000 c) 1500000 d) 1600000

16) According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts for 20% of the total FDI 

a) $30m b) $9m c) $60 m d) none

17) If in question 16, the growth in the size of FDI for the next year with respect to the previous year is 20%, then find the share of urban Maharashtra next year if 12% of the total FDI going to Maharashtra went to urban areas (provided Maharashtra attracted only 10% of the total share for both years)

a) $36m b) $4.32m c) $3m d) none 

18) The cost of food accounted for 25% of the income of a particular family. If the income gets raised by 20%, then what should be the percentage point decrease in the food expenditure as a percentage of the total income to keep the food expenditure unchanged between the two years?

a) 3.5 b) 8.33 c) 4.16 d) 5

19) If the length, breadth and height of a cube are decreased, decreased and increased by 5%, 5% and 20% respectively, then what will be the impact on the surface area of the cube (in percentage terms)

a) 7.25% b) 5% c) 8.33% d) 6.0833%

20) A's salary is first increased by 25% and then decreased by 20%. The result is the same as B's salary increased by 20% and then reduced by 25%. Find the ratio of B's salary to that of A's ?

a) 4:3 b) 11:10 c) 10:9 d) 12:11

21) The minimum quantity of milk in litres (in whole number) that should be mixed in a mixture of 60 litres in which the initial ratio of milk to water is 1:4 so that the resulting mixture has 15% milk is

a) 3 b) 4 c) 5 d) This is not possible 

22) A person saves 6% of his income. Two years later, his income shoots up by 15% but his savings remain the same. Find the hike in his expenditure.

a) 15.95% b) 15% c) 14.8% d) none 

23) A is 50% more than B, C is 2/3 of A and D is 60% more than C. Now, each of A, B, C and D is increased by 10%. Find what percent of B is S(after the increase)?

a) 150% b) 160% c) 175% d) 175%

24) A and B have, between them, Rs 1200. A spends 12% of his money while B spends 20% of his money. They are then left with a sum that constitutes 85% of the whole sum. Find what amount is left with A.

a) 750 b) 800 c) 700 d) 660

25) Maya has Rs M with her and her friend Chanda has Rs C with her. Maya spends 12% of her money and Chanda also spends the same amount as Maya did. What percentage of her money did Chanda Spend?

a) 18M/C b) 18C/M c) 12M/C d) 12C/M

26) In a village consisting of p persons, x% can read and write. If the males alone y%, and of the females alone. z% can read and write. Find the number of males in the village in terms of p, x, y and z if z< y.

a) p(x - z)/(y+ x - z)

b) p(x - z)/(y+ x - 2z)

c) p(y - x)/( x - z)

d)  p(x - z)/( y - z)

27) In order to maximize his gain, a theatre owner decides to reduce the price of tickets by 20% and as a result of this, the sales of tickets increase by 40%. If, as a result of these changes, he is able to increase his weekly collection by Rs 168000, find by what value did the gross collection increase per day?

a) 14000 b) 18000 c) 24000 d) 20000

28) In a town consisting of three localities A, B, C, the population of the three localities A, B and C are in the ratio 9:8:3. In locality A, 80% of the people are literate, in locality B, 30% of the people are illustrate. If 90% people in locality C are literate, find the percentage literacy in that town?

a) 61.5% b) 78 % c) 75% d) none 

29) A fraction is such that if the double of the numerator and the triple of the denominator is changed by +19% and -30% respectively then we get 11% of 16/21. Find the fraction.

a) 4/25 b) 2/25 c) 3/25 d) none 

30) To pass an examination, 40% marks are essential. A obtains 10% marks less than the pass marks and B obtains 11.11% marks less than A. What percent less than the sum of A's and B's marks should C obtain to pass the examination.

a) 40% b) 41(3/17)% c) 28% d) any of these 

31) The hourly wages of a female labour are increased by 12.5%, whereas the weekly working hours are reduced by 8%. Find the percentage change in the weekly wages if she was getting Rs 1200 per week for 50 hours previously.

a) +3.5% b) 4% c) 4.5% d) none 

32) Two numbers X and Y are 20% and 28% less than a third number Z. Find by what percentage is the number Y less than the number X ?

a) 8% b) 12% c) 10% d) 9%

33) Price of a commodity is first increased by x% and then decreased by x%. If the new price is K/100, find the original price.

a) (x -100)100/K

b) (x² -100²)100/K

c) (100 -x)100/K

d) 100K/(100²- x²)

34) The salary of a person is increased by Rs 4800 the rate of tax is decreased by 2% from 12% to 10%. The effect is such that he is now paying the same tax as before. If in both the cases, the standard tax deduction is fixed at 20% of the total income, find the increased salary?

a) 32800 b) 36800 c) 28000 d) none 

35) Reena goes to a shop to buy a radio costing Rs 2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs 2568 inclusive of sales tax. Find the reduction in the price of the radio.

a) 180 b) 210 c) 168 d) none 

* Directions for 36-38

 In a recent youth organised by AMS Careers, the entry tickets were sold out according to the following scheme:

Tickets.             6      12      18

Discount%      10%   20%    25%

Original price per ticket: Rs 40

This offer could have been availed only when tickets were bought in a fixed lot according to the scheme and any additional ticket was available at its original price.

36) If a person has to buy 25 tickets, then what will be minimum price per ticket?

a) equal to Rs 32 

b) 32.31

c) 31.84 d) can not determined 

1c 2b 3d 4b 5c 6c 

%

PROFIT , LOSS & DISCOUNT 

EXERCISE - A

1) A person purchased a vehicle for Rs590828 and sold it for 652920. What is the profit percent he earned on this vehicle (correct to two decimal places)?

a) 10.51% b) 9.55% c) 9.51% d) 11.5%

2) Selling price of a table is Rs2808. If profit percent is 17%, then what is the cost price(in Rs) of table ?

a) 2288 b) 2300 c) 2400 d) 3285

3) The difference between cost price and selling price is Rs12.54. If loss percentage is 33%, then what is the cost price (in Rs)?

a) 35.44 b) 50.54 c) 41  d) 38 

4) if the cost price of an article is 75% of its selling price, then what will be the profit percentage ?

a) 23.47  b) 25 c) 33.33 d) 20 

5) cost price of a watch is Rs530. If the loss percentage is 24%, then what is the value of loss ?

a) 127.2 b) 15³.2 c) 139.4 d) 114.2

6) A vendor buys oranges @ 5 for Rs6 and sales at the rate of 2 for Rs3. What will be the result ?

a) 25% loss b) 25% gain  c) 20% gain d) 20% loss 

7) A shopkeeper by selling 20 Timex watches, earns  a profit equals to the selling price of four Timex watches.  His profit percentage is

a) 20%  b) 25% c) 40%  d) 15%

8) The marked price of an article is 10/7 of the cost price and the selling price of that article is 4/5 of the marked price . What is the profit percent .

a) 17.24  b) 16.66 c) 14.28 d) 15.42 

9) Selling price of a glass is Rs1965 and loss percentage is 25%. If the selling price is Rs3013, then what will be the profit percent ?

a) 13  b) 10.4 c) 15 d) 20 

10) Punit purchases 5 dozen of oranges at the rate of Rs120 per dozen . He sold each one of them at rate of Rs11.5 . What is the profit (in percentage) of Puneet ?

a) 18 b) 30 c) 12 d) 15 

11) The ratio of selling price to the cost price is 13:17. What is the loss percentage ?

a) 23.52 b) 27.74 c) 18.62 d) 19.45

12) Two pens are bought at the rate of Rs20 each. Shopkeeper sells one at the profit of 25% and other at the loss of 25%. What will be the total profit or loss on the whole transaction ?

a) no profit/no loss b) profit 1 rupees c) loss 1 rupees d) loss of two rupees

13) A man bought 3 articles for Rs6000 each . He sold the articles respectively at 15% profit , 12% profit and 15% loss. The total percentage profit/loss he earned is

a) 4% profit  b) 3% loss c) 10% profit  d) 3% profit 

14) An article is sold for Rs x. If it is sold at 100/3% of this price, there is a loss of 20%. What is the percentage profit when it is sold for Rs. x ?

a) 140 b) 125 c) 130 d) 120 

15) Three articles are bought at Rs200 each. one of them is sold at a loss of 10%. If the other two articles are sold as to gain 20% on the whole transaction, then what is the gain% on the two articles ?

a) 28  b) 32  c) 35  d) 30 

16) A trader had 6 quintals of wheat. He sold a part of it at 7% profit and the rest at 17% profit, so that he made a total profit of 11%. How much wheat did he sale at 17% profit

a) 360 kg b) 240 kg  c) 120 kg d) 480 kg 

17) A rice trader buys 25 quintal of rice for Rs1825, 27% rice is lost in transportation. At what rate should he sale to earn 20% profit ?

a) Rs44.4 per quintal b) Rs120 per quintal c) Rs87.6 per quintal d) 115.8 per quintal

18) Rahul sales a machine for Rs50 lakhs at a loss. Had he sold it for Rs60 lakhs,  his gain would have been 7 times the earlier loss. What is the cost price of the machine?

a) 51.25 lakhs b) 58.75 lakh c) 67.14 lakh d) 43.75 lakh 

19) A wholesaler sales a watch to a retailer at a gain of 32% and the retailer at a profit of 32% and the retailer sell it to a customer at a loss of 20%, if the customer pays Rs1953.6, what had it cost the wholesaler ?

a) 2063 b) 2394  c) 1850 d) 1637 

20) The total cost of a dishwasher with a vacuum cleaner was Rs78750. The vacuum cleaner was sold at a profit of 37% and the dishwasher at a loss of 27%. If the sell price was the same in both the items, then the cost price of the cheaper item was 

a) 51375  b) 29375 c) 30750  d) 27375 

21) Marked price of an article is Rs3600 and selling price is Rs3132. What is the discount percentage ?

a) 12% b) 13% c) 17.21% d) 14.94% 

22) 10% discount is offered on an item. By applying a promo code the customer wins 4% cashback. What is effective discount ?

a) 33.6% b) 30% c) 22% d) 13.6% 

23) a man get a discount of 30% and then 20% on his food bill of Rs1250. How much amount does he has to pay ?

a) 700 b) 560 c) 350 d) 500 

24) There was 29% off on bags lady. A lady bought a bag and got 12% discount for paying in cash . She paid Rs 312.40. What is the price tag in rupees on the bag 

a) 600 b) 625 c) 450 d) 500 

25) an article is sold for Rs688.16 after 2 successive discounts of 12% and 8% respectively. What is its marked price ?

a) 800 b) 900  c) 820 d) 850

26) Three successive discounts on the marked price of an article turns out to be equivalent to a single discount of 19%. If the rates of the first and second discount are 10% and 4% respectively, what is the rate of the third discount ?

a) 7.50% b) 5.25%  c) 6.25% d) 6.00%

27) The marked price of a helmet is 30% more than its cost price. If the helmet is sold for Rs744 after a discount of Rs36, then what will be the profit percentage?

a) 24  b) 18 c) 21 d) 27 

28) Abhishek marks the price of his laptop 60% above the cost price. if he gives a discount of 30% of the marked price, then what is the profit percentage?

a) 30  b) 12 c) 15 d) 14 

29) The Marked price of an article is Rs600. After allowing a discount of 25% on the marked price, there was a loss of 30 rupees. The loss percentage is

a) 7.50%  b) 7.25% c) 6.25% d) 6.50%

30) The cost price of an article is Rs425, A shopkeeper gives a discount of 20% and still gains 16%. What is the marked price of the article?

a) 605.75 b) 620.50 c) 624.50 d) 616.25 

31) Rohit wants to 21% profit on a belt after offering 45% discount. By how much percentage more should he mark the price of his article above the cost price ?

a) 75.45 b) 120 c) 102.5 d) 66 

32) A dealer buys an article marked at  Rs3000 with two successive discounts of 20% and 5%. He spends Rs1200 on repairs and sells it for Rs30000. What is his profit or loss percent 

a) 25% loss b)  25% profit c) 20% profit d) 20% loss 

33) At 24% discount the selling price of a washing machine is Rs38000. What is the selling price if the discount is 40% ?

a) 18000 b) 30000  c) 22320 d) 31920

34) Hiten  marks his pen at Rs9800 and after allowing discount at 20%, he still earns 12% profit. What is the cost price of the pen?

a) 7600 b) 7200 c) 6500 d) 7000 

35) At 13% discount the selling price of an oven is Rs18000, what is the selling price if the discount is 27.5%

a) 10875  b) 12828.75 c) 15000 d) 16638.75 

36) When a discount of 25% is given on a wedding gown, the profit is 32%. If the discount is 17%,  then the profit is

a) 46.08%  b) 49% c) 51.92% d)!43.16% 

37) If a Merchant offers a discount of 4% on the list price, then she makes a loss of 10%. What percentage what percentage profit or loss will she make if she sells at a discount of 20% of the list price ?

a) 25% loss b) 4% loss c) 50% profit d) 26% profit

38) Marked price of an item is Rs400. On purchase of 1 item discount is 6% and on purchase of four items discount is 24%. Rachita buys 5 items, What is the effective discount ?

a) 34%  b) 24.4%  c) 12.8%  d) 23.25%

1a 2c 3d 4c 5a 6b 7b 8c 9c 10d 11a 12a 13a 14a 15c 16b 17b 18a 19c 20d 21b 22d 23a 24d 25d 26c 27a 28b 29c 30d 31b 32b 33b 34d 35c 36a 37a 38b

EXERCISE - B

1) Ram sold a motorcycle for Rs70000 at 25% profit. For what price should he sale a motorcycle to gain 30% profit ?

a) 72700 b) 72900 c) 72900 d) 72600

2) List the price of a bike is 15% more than it's cost price. It is sold at a discount of 20%. Find the dealer's loss or profit percent.

a) profit 8% b) profit 9% c) loss 9% d) loss 8% 

3) When an article is sold for Rs291, there is a loss of 3%. What will be the selling price of the article, if it is sold at a gain of 8%?

a) 308 b) 332  c) 324 d) 316 

4) The total cost of two articles is Rs2000. One of them is sold at a profit of 12% and the other at a loss of 12%. The overall gain in the transaction is 1.2%. The cost price of the article for which there was a profit of 

a) 1050 b) 1100 c) 1120 d) 1080

5) A man losses 20% by selling an article for Rs 96. For what amount should he have sold the articles to gain 15% ?

a) 120 b) 115 c) 138 d) 140

6) A man bought three articles for Rs3000 each . He sold the articles respectively at 15% profit , 10% profit and 15% loss. The total percentage profit/loss he earned is 

a) no profit no loss b) 10/3% profit c) 10/ 3% loss d) 10% loss

7) A purchased two articles for Rs200 and  Rs300 respectively and sold at gain of 5% and 10% respectively. What was his overall gain percentage ?

a) 6 b) 9 c) 5 d) 8 

8) After allowing a discount of 10% on the marked price of an article, it is sold for Rs360.  Had the discount not been given, the profit would have been 25%. What is the cost price of the article ?

a) 350 b) 360 c) 320 d) 325 

9) By selling an article for Rs144, a shopkeeper losses 28%. What should be the selling price for bringing down the loss to 14% ?

a) 156  b) 182 c) 172 d) 180 

10) An article is sold for Rs360 after allowing discount of 20% on its Marked price. Had the discount not been allowed , the profit would have been 50%. The cost price of the article is .

a) 320  b) 300 c) 360 d) 350

11) A person purchased a vehicle for Rs489823 and sold it for Rs589828. What is the profit percent he earned on this vehicle (correct to two decimal places)?

a) 25% b) 18.65% c) 20.42% d) 15% 

12) Two items are sold for Rs18602 each. On one item there has been a gain of 31% and so on the second item a loss of 29%. What was the overall loss or gain in the transaction ?

a) loss 7.91%  b) loss 8.21% c) gain 8.25% d) gain 7.91% 

13) By selling an article for Rs2300 Rekha gains 25%. If she sells it for Rs1955, then her loss/gain percentage is

a) loss 6.5%  b) gain 6.5% c) gain 6.25% d) loss 6.25%

14) A shopkeeper bought an article for Rs100 and marked its price 25% above the cost price. How much discount percentage should he announce in order to make a profit of 15%?

a) 8.25 b) 8.5 c) 8  d) 10 

15) An article is marked at a price which is 1.2 times its cost price. After allowing a certain discount on the marked price, the profit reduces to 10%. The discount percentage is 

a) 25/3 b) 9 c) 10 d) 26/3 

16) A trader sales wire and gains 60% on the cost price. What will be the profit percentage on selling price ?

a) 33.33  b) 40 c) 37.5 d) 60

17) if two successive discount of 25% and 30% are given, then what will be the ratio of the marked price to selling price ?

a) 20 :7 b) 40 :21 c) 20 :17 d) 40:33 

18) The difference between the cost price and selling price is Rs221. If profit percentage 17%. Then what is the selling price.

a) 1079 b) 1300 c) 1521 d) 1724 

19) Ramesh marks his articles at Rs6000 and after allowing a discount of 20%, he still earns 60% profit. What is the cost price of the article?

a) 3600 b) 4800 c) 3000 d) 4200

20) Rohit buys a ball for Rs450 and sales it. Rohit gives two successive discount of 20% and 5% to the customer. What will be the selling price of the ball ?

a) 342  b) 354 c) 334  d) 362 

21) The marked price of a chair is 40% more than its cost price. If the chair is sold for Rs520 after discount of Rs40, then what will be the profit percentage ?

a) 33 b) 40 c) 25 d) 30

22)A shopkeeper wants to earns 33% profit on an article after offering 30% discount. By how much percentage more he should mark the price of his article above cost price ?

a) 90 b) 63 c) 69 d) 72

23) Daily ticket of a local train cost Rs140 and monthly pass costs Rs3276. If Mohan buys the monthly pass and travel for 30 days in a month, then what amount does he save ?

a) 18% b) 16% c) 15% d) 22% 

24)  Selling price of a chair is Rs1386. If loss percentage is 23%, then what is the cost price of chair.

a) 1600 b) 1800 c) 1900 d) 1067

25) The difference between the cost price and selling price is Rs576. If the profit percentage is 16%, then what is the cost price?

a) 3024 b) 4176 c) 3600 d) 3800

26) Raj sells a machine for Rs51 lakhs at a loss. Had he sold it for Rs60 lakhs, his gain would have been 8 times the earlier loss. What is the cost price of the machine.

a) 59 lakhs b) 52 lakhs c) 66.375 lakhs d) 45 lakhs

27) A vendor buys chikoos at 15 for Rs8 and then sells at 10 for Rs6. What will be the result ?

a) 12.5% loss b) 11.11% gain c) 12.5% gain d) 11.1% loss

28) A vendor bought 40 dozen of fruits for Rs2400. Out of these, 30 fruits were rotten and thrown away. At what rate per dozen should he sells the remaining fruits to make a profit of 25%?

a) 84 b) 72 c) 90 d) 80

29) Rahul professes to lose 16% on selling sugar and uses a weight of 680gm instead of 1 kg. What is the total profit percentage ?

a) 23.52 b) 16 c) 28.57 d) 19.24 

30) Marked price of an article is Rs 520 and selling price is Rs384.8.  What is the discount percentage ?

a 24.42 b) 26 c) 35.13 d) 29

31) 20% discount is offered on item. By applying a promo code the customer wins 30% cash back. What is the effective discount 

a) 44% b) 30% c) 32% d) 22% 

32) A shopkeeper decides to raise the marked price of an article by 10%. How much discount should he allows so as be able to sell the article of the original marked price?

a) 100/11% b) 73/9% c) 19/2% d) 10%

33) if a merchant offers discount of 20% on the list price, then she makes a loss of 16%. What percent profit or percent loss will she make if she sells goods at a discount of 10% of the list price ?

a) 14% profit b) 20% profit c) 50% profit d) 5.5% loss 

34) There was 25% off on shirt. A lady bought that shirt and got an additional 20% discount for paying in cash and further 10% discount for being a loyal customer. She paid Rs324. What is the price tag on the shirt

a) 650 b) 725 c) 600 d) 750

1c 2d 3c 4b 5c 6b 7d 8c 9c 10b 11c 12a 13c 14c 15a 16c 17b 18c 19c 20a 21d 22a 23d 24b 25c 26b 27c 28d 29a 30b 31a 32a 33d 34c

PARTNERSHIP 

EXERCISE - A

1) Seema, Sonia and Akshita opened shop in partnership with their investments Rs27000, Rs81000 and Rs72000 respectively. Profit was distributed between them at the end of the years. If share of Sonia's is Rs36000 in profit, then total profit was..

a) 80000 b) 98000 c) 108000 d) 116000

2) A and B started a business by investing Rs10400 and Rs14300 in partnership. After 4 months C had joined them by investing Rs9100. If total profit in the end of year was Rs11360, then share of C in profit was

a) 2520 b) 2²40 c) 2660 d) 2100 

3) U and V started a business by investing amounts Rs184000 and Rs224000 respectively. If U's share in the profit received at the end of the year is Rs20700, then what will be the total profit earned by them together 

a) 43200 b) 45900 c) 52300 d) 56400

4) A, B and C invested Rs26000, Rs34000 and Rs10000 respectively in a business. At the end of the year, they earn a profit of Rs3500. B's share of profit is

a) 1200 b) 1500 c) 1700 d) 1900

5) Rs4800 is distributed among A, B and C in the ratio of 6: 5: 4. The difference in the shares of A and C is

a) 3200 b) 640 c) 500 d) 675 

6) A, B, C subscriber Rs50000 for a business. A subscribes Rs4000 more than B and B Rs5000 more than C. Out of the total profit Rs35000, A receives 

a) 8400 b) 11900 c) 13600 d) 14700 

7) S, T,and U started a business and their capitals are in the ratio of 3:4:6. At the end they receive the profit in the ratio 1: 2 :3. What will be the respective ratio of time period for which they contributed their capitals ?

a) 3:2:2 b) 2:3:3  c) 2:2:3  d) 4:5:3 

8) A and B invest in the ratio 3:5. After 6 months , C joins the business investing an amount equals to B's. At the end of the year, what will be the ratio of their profits?

a)6:10:5 b) 3:5:2 c) 8:10:5 d) 3:5:5

9) U starts a business by investing Rs45000 and V joined him after 1 year with an amount of Rs33000. After 2 years from the starting of business, they earned profit of Rs16400. What will be the U's share in the profit?

a) 11200 b) 9600 c) 10000 d) 1200 

10) Lokesh starts a business with Rs240000. After 3 months Vishal joins him with Rs210000. At the end of the year what will be the ratio of their profits?

a) 32:21 b) 16: 13  c) 8: 5 d) 45 :39

11) A started a business with the capital of Rs1800. After 4 months, B joined with Rs3600. 6 months after the business started C  joined with Rs1200. If the total profit earned at the end of the year is Rs1760, then what is the share of A?

a) 540  b) 660 c) 840 d) 720

12) S, T, and U started a business by besting Rs4200, Rs6300 and Rs8400 respectively. S left the business after 3 months, T left 6 months after the business had started U remained in the business till ine year. At the end of 1 year the total profit is Rs6000. What is the U's share in the profit ?

a) 4200 b) 3200 c) 4200 d) 3600

13) A and B started a business with initial investments in the ratio 12:11 and their annual profits were in the ratio 4:1. If A invested the money for 11 months, B invested the money for 

a) 3 months  b) 4 months c) 5 months d) 7 months 

14) Rohit started a business with Rs75000 and after some months Simran joined him with Rs60000. If the profit in the ratio 3:1, then after how many months did simran join Rohit?

a) 7 b) 6 c) 8 d) 4

15) P and Q invested some money in a business in the ratio of 4:7 respectively. After 6 months P withdraws his capital. If they receive profits in the ratio 4:21, then for how many months did Q invest in the business ?

a) 12 b) 15  c) 18 d) 19

16) Amitabh, Brijesh and Kamlesh enter into a partnership with shares in the ratio 7/2 : 4/3 : 6/5. After 4 months Amitabh increases his share by 50%. If the total profit at the end of the year is Rs 21600, then what will be the share of Brijesh in the profit?

a) 8000 b) 12000 c) 4000 d) 7000 

17) Profit of 277200 has divided among three partners Abdullah, Bhanudas and chakor in the ratio 3:6:2 how much year in chakra Gates 500005625200 ABC started business by investing 3:6:2. How much share Chakor gets?

a) 50400 b) 151200 c) 75600 d) 25200

18) A, B and C started a shop by investing Rs36000, Rs81000 and Rs63000 respectively. At the end of one year. B's share of total profit was Rs36000. What was the total profit ?

a) 108000 b) 116000 c) 80000 d) 16200

1b 2c 3b 4d 5b 6a 7d 8a 9b 10c 11a 12a 13c 14c 15a 16c 17a 18b 

SIMPLE & COMPOUND INTREST 

EXERCISE - A

1) Simple interest on a sum for 6 months at the rate of 5% per annum is Rs65.5. What is the value of sum?

a) 2600 b) 2620 c) 1320 d) 2880

2) A person borrows some money for 8 years at the rate of simple interest. If the ratio of principal and total interest 5:8, then what is the rate (in percentage) of interest?

a) 10 b) 20 c) 25 d) 30 

3) simple interest on a sum of 5 years is equals to 20% of the principal. In how many years interest will be equal to the principal ?

a) 20 b) 25 c) 15 d) 16 

4) Deepak land Rs8800 to Jaichand for 13 year and Rs5500 to Kapil for 12 years on simple interest at the same rate of interest and received Rs14432 in all from both of them as interest. The rate of interest per annum is 

a) 8.5% b) 9% c) 9.5% d) 8%

5) The simple interest on a sum for 8 years is Rs47500. The rate of interest for the first 5 year is 10% per annum and for the next 3 years is 15%. What is the value of sum?

a) 50000 b) 60000 c) 45000 d) 62500

6) A sum of Rs8000 is divided into two parts. The simple interest on first part at the rate of 21% per annum is equals to the simple interest on second part of the rate of 35% per annum is equal to the simple interest on second part at the rate of 35% per annum. What is the interest of ech part.

a) 1050  b) 840  c) 1400 d) 1220

7) A sum becomes Rs2286 in 3 years and Rs2448 in 4 years at simple interest. What is the rate (in percentage) of intrest per annum?

a) 10 b) 9 c) 8 d) 11 

8) A sum of Rs1200 amount to Rs1740 in 3 years at simple interest. If the rate of interest is increased by 3%, then what will be the new amount ?

a) 1848  b) 1946 c) 1812 d) 1924 

9) A certain sum was invested on simple interest. The amount to which it had grown in 5 years was 5/4 times the amount to which it had grown in 3 years. The percentage rate of interest was 

a) 20 b) 25 c) 33 d) 50 

10) A borrowed a sum of Rs3000 from his friends B on 31st December 2007 on the condition that he would return the same after 1 year with simple interest at 15% per annum. However, A gets into a position of returning the sum on 31st August 2008. How much amount had A return to B ?

a) 3330 b) 3200 c) 3310 d) 3305 

11) At what rate of compound interest per annum will a sum of Rs50000 becomes Rs73205 in 2 years

a) 21% b) 19% c) 17% d) 15% 

12) A sum is invested for 3 years at compound interest at 5%, 10% and 20% respectively. In 3 years, If the sum of the amounts to Rs16632, then find the sum.

a) 11000 b) 12000 c)  13000 d) 14000 

13) A sum of Rs2000 becomes Rs3645 in 2 years at a certain rate of compound interest. What will be the sum (in Rs) after 4 years ?

a) 5942.125  b) 6643.0125 c) 7243.0125 d) 7498.125

14) An amount at compound interest doubles itself in 4 years. In how many years will the amount become 8 times itself ?

a) 8 year b) 12 year c) 16 year d) 24 year

15) What is the compound interest on a sum of Rs4096 at 15% per annum for 5/2 year, if the interest is compounded to 10 monthly ?

a) 1726 b) 1736 c) 1636 d) 1763 

16) A Bank offer 15% compund intrest per half year. A customer deposits Rs2400 each on 1st January and 1st July of a year. At the end of the year, the amount he would have given by way of interest is 

a) 2268 b) 1134 c) 567 d) 283 

17) Rs60000 invested at a certain rate for a certain even number of years, compounded annually, grows to Rs63654. To how much amount would it grow if it is invested at the same rate for half the period ?

a) 61800 b) 61809 c) 61675 d) 61827

18) If the amount received at the end of second and third year at compound interest on a certain principle is Rs30250 and 33275 respectively. What is the rate of interest ?

a) 10% b) 5% c) 20% d) 16% 

19) compound interest on a certain sum for 2 years at the rate of 11% per annum is Rs1160.5. What will be the simple interest for the same amount at the same rate of interest for 2 years.

a) 9000 b) 1000 c) 1100 d) 1050

20) The compound interest on a certain sum of money at 21% for 2 years is Rs11602.5. Its simple interest at the same rate and for the same period is

a) 10750  b) 16000 c) 12500 d) 10500 

21) On a certain principal if the simple interest for 2 years is Rs4800 and compound interest for 2 years is Rs5088, what is the rate of interest ?

a) 6% b) 24% c) 12% d)18%

22) Simple interest on certain sum of money 3 years at 8% per annum is half the compound interest on Rs1600 for 2 years at 10% per annum. The sum placed on simple interest is

a) 14000 b) 3500 c) 7000 d) 5600 

23) There is 75% increase in an amount in 5 years at the simple interest. What will be the compound interest of Rs40000 after 2 year at the same rate?

a) 25800 b) 32250 c) 12900 d) 19350

24) The simple interest on a certain sum for 7/2 year at 10% per annum is Rs2940. What will be the compound interest on the same sum for 5/2 year at the same rate when interest is compounded yearly (nearest to a rupees)

a) 2272 b) 2227  c) 2327 d) 2372

25) A sum of 7500 amounts to Rs8748 after 2 year at a certain compound interest rate per annum. What will be the simple interest on the same sum for 23/5 year at double the earlier interest rate ?

a) 4140  b) 5520 c) 8180 d) 2760

26) The compound interest on a certain sum for 3 years at 15% per annum intrest compounding yearly is Rs4167. What is the simple interest on the same sum in 24/5 year at the same rate ?

a) 6144 b) 6000 c) 4800 d) 5760 

27) A sum of Rs10000 amounts to Rs11664 in 2 years at a certain rate percent per annum, when the interest is compounded yearly. What will be the simple interest on the same sum for 27/5 at the same rate ?

a) 4320 b) 4160 c) 3840 d) 4040

28) An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding ). The sum of interest obtained after 2 years from both the schemes is Rs2961. If both schemes have  23% per annum interest rate, then what is the first interest of simple interest scheme.

a) 500 b) 1100 c) 700 d) 900 

29) What is the difference between the compound interest, when the interest is compounded 5 monthly and the simple interest on a sum of Rs12000 for 5/4 years at 12% per annum?

a) 90 b) 91.50 c) 93 d) 92.50

30) The difference between simple and compound interests compounded annually on a certain sum of money for 2 year at 9% p.a., annum is Rs 405. The sum is

a) Rs 5000 b) Rs 100000  c) Rs 200000 d) Rs 150000

31) The difference between simple interest and compound interest compounded annually on a certain sum of money for 2 years at 16% per annum is Rs320. What is the value of given sum?

a) 25000 b) 50000 c) 37500 d) 12500 

32) The difference between the compound interest and the simple interest on a sum at 10% per annum for 3 years is Rs 155. The sum is

a) 5500 b) 6000 c) 6600 d) 5000

33) A scooty is sold by an automobile agency for Rs19200 cash or for Rs4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12% per annum, then the value of each installment (approximately in Rs) is 

a) 3125  b) 2965  c) 2800 d) 2825 

34)  A sum of Rs11000 was taken as loan. This is to be paid in two equal annual installments . If the rate of interest is 20% compound annually. then the value of each installment is

a) 7500 b) 7000 c) 7100 d) 7200

1b 2b 3b 4d 5a 6a 7b 8a 9a 10a 11a 12b 13b 14b 15b 16b 17a 18a 19c 20d 21c 22c 23c 24a 25b 26d 27a 28c 29b 30a 31d 32d 33b 34d 

 

EXERCISE - B

1) A sum of Rs10000 is invested on simple interest at the rate of 5% per annum for 10 years. What is the total interest of the 10 year ?

a) 4000 b) 5000 c) 2500 d) 4500

2) A sum becomes Rs8800 in 4 years at simple interest at the yearly interest rate of 25% per annum. What is the sum?

a) 4400 b) 6600 c) 7040 d) 6400

3) Simple interest on a sum of Rs1400 for 3 years and 4 months is Rs700. What is the rate (in percentage) of interest per annum ?

a) 17 b) 15 c) 18 d) 12

4) The compound interest on a certain sum of money for 2 years at 5% is  Rs328, then the sum is 

a) 3000 b) 3600 c) 3200 d) 3400 

5) At what rate of compound interest per annum will a sum of Rs2000 becomes Rs23328 in 2 years ?

a) 8% b) 16% c) 24% d) 12% 

6) Rs10000 is kept at compound interest at the rate of 18% per annum compounding annually. If the compounding of interest is done half yearly, then how much more interest will be obtained ?

a) 243 b) 324 c) 81 d) 162 

7) What annual installment will discharge dept of Rs1696 in 4 years at 4% per annum simple interest ?

a) 525 b) 425 c) 325 d) 400

8) In how many years shall Rs3500 invested the rate of 10% simple interest per annum, amount to Rs4500 ?

a) 19/5yr b) 17/7yr c) 18/7yr d) 20/7yr

9) A borrows a sum Rs1000 from his friends B on 31st December 2015 on the condition that he will return the same after 1 year with simple interest at 12%. However , A gets into a position of returning the money on 1 May 2016. How much amount he has to return to B?

a) 1331.5 b) 1045 c) 1120 d) 1040

10) A certain amount invested at a certain rate, compound annually, grows to an amount in 5 years, which is a factor of 1.1881 more than to what it would have grown in 3 years. What is the rate percentage?

a) 9  b) 8.1 c) 8 d) 9.2 

11) The difference between compound interest and simple interest on Rs x at 6.5% per annum for 2 years is

a) 7800 b) 7500 c) 8000 d) 8500

12) The compound interest on a certain sum of money at 21% for 2 years is 9282, its simple interest at same rate and for the same period is 

a) 8750 b) 8400 c) 8000 d) 8500 

13) simple interest on a sum for 8 months at 6% per annum is Rs340. What is the value of sum ?

a) 8500 b) 9500 c) 8000 d) 6800

14) A sum becomes Rs1392 in 2 years and Rs1488 in 3 years at simple interest. What is the rate (in percentage) of interest per annum ?

a) 8 b) 10 c) 12 d) 8.5 

15) A person borrows some money for 4 years at the rate of simple interest. If the ratio of principle and total interest is 5:1, then what is the rate of interest?

a)  5 b) 25 c) 10 d) 20

16) A sum of Rs7500 is divided into two parts. The simple interest on first part at the rate of 12% per annum is equal to the simple interest on second part at the rate of 18%. What is the interest on each part of 1 year ?

a) 600 b) 360 c) 480 d) 540 

17) An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The total interest obtained after 2 years from both the schemes together is Rs2090. If both the schemes have 18% per annum interest rate, then what is the first year interest scheme?

a) 1000 b) 500 c) 545 d) 1045

1b 2a 3b 4c 5a 6c 7d 8d 9d 10a 11c 12b 13a 14a 15a 16d 17b 

MIXTURE AND ALLIGATION

EXERCISE - A

1) In What ratio salt costing Rs13 per kg mixed with another salt costing Rs7 per kg to get a mixture costing Rs9 per kg 

a) 4:7 b) 3:5 c) 2:3 d) 1 :2

2) Two mixtures have milk and water in the ratio 1: 4 and 3:2 respectively. In what ratio two types of mixture have to be mixed to get a new mixture having ratio of milk and water as 1:1 ?

a) 4:3 b) 5 :3 c) 3: 2 d) 1:3

3) In a mixture of milk and water, there is 19% milk. If the quantity of milk in the mixture of 437ml, then what is the total quantity (in millimetres) of mixture?

a) 2300 b) 2200 c) 2100 d) 2400

4) How much water must be added to a bucket which contains 40 litera of milk at the cost price of Rs3.50 per litre, so that the cost of milk reduces to Rs2 per litre ?

a) 25 b) 28 c) 30 d) 35 

5) A confectioner sells the milk after mixing some water in it at the same rate at which he bought. If he gains 25% on his way, the quantity of water mixed with per litre of milk is

a) 0.25 b) 2.5 c) 1.5 d) 0.35 

6) In what proportion must water be added to spirit to gain 20% by selling it at the cost price ?

a) 2:5 b) 1:5 c) 3:5 d) 4:5

7) In what ratio sugar of Rs38 per kg and Rs30 per kg and be mixed with each other so that on selling mixture at Rs 35.2 per kg there will be a gain of 10%?

a) 1:3 b) 3:7 c) 13:7 d) 9:4

8) In a mixture of 35L, the ratio of milk and water is 4:1. If 7 L of water is added to mixture, then the new ratio will be

a) 2:1 b) 1:2 c) 3:2 d) 2:3 

9) A container has 84 L of mixture consisting of milk and water in the ratio 5:2. To make this ratio 2:1, the quantity of more water required to be added will be

a) 2 litre b) 4 c) 6 d) 8 

10) A veriety of rice at Rs14 per kg is mixed to Rs15 kg of another variety rice at Rs20 per kg, so as to make a mixture worth Rs 16.50 per kg. The quantity of a rice at Rs14 per kg must be 

a) 5 kg b) 7 kg c) 15kg d) 21 kg 

11) The milk and water in two vessels are in the ratio 3:1 and 7 : 11, respectively. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture containing half milk and half water?

a) 5:7 b) 4:9 c) 1:1 d) 4:7

12) two vessels of equal capacity contains juice and water in the ratio 5 :1 and 5:7 respectively. The mixture of both the vessels are mixed and transferred in to a bigger vessel. What is the ratio of juice and water in the new mixture?

a) 3: 2 b) 5:3 c) 5:4 d) 1:2

13) A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloys C, the ratio of gold and copper in C will be 

a) 5:7 b) 5 :9 c) 7 :5 d) 9 :5 

14) A milkman has two types of milk. In one, the percentage of water is 10 and in the second the percentage of water is 20. If he takes 90 litre milk of type I and 60L of milk of type II and prepares a new mixture, the percentage of water in this new mixture is

a) 12% b) 14% c) 15% d) 19% 

15) The ratio of milk and water in 3 samples is 1:3, 3:5 and 11:5. A mixture containing equal quantities of all three samples is made. What will be the ratio of milk and water in the new mixture?

a) 7:9 b) 5:7 c) 15:13 d) 9:11

16) The alcohol and water in a mixture are in the ratio 7:8 respectively. If 11 litre water is added to it, then the ratio of alcohol and water in the new mixture becomes 3: 5. What is the total quantity( in litres) of the alcohol in the new mixture ?

a) 21 b) 24 c) 35 d) 32

17) A milkman uses three containers for the selling milk , their capacities being 40L, 30L and 20L respectively. He fills respectively 87.5%, 80% and 90% of the container with the mix of milk and water in the ratio 3:2, 5:1 and 7:2 respectively. What is the ratio of the total quantity of milk to that of water carried by him ?

a)  7:2 b) 31:12 c) 35: 9 d) 5:2

18) In what ratio must a mixture of 20% milk be mixed with that of 60% milk strength so as to get a new mixture 25% milk strength?

a)  7:1 b) 4 :1 c) 5 :2 d) 9:2

19) 20kg of a mixture of wheat and husk contains 5% husk . How many kilograms more of husk must be added to make the husk content 20% in the new mixture ?

a) 2.75  b) 3.75 c) 4. 75 d) 5.75

20) In an alloy aluminium and tin are in the ratio of 4:5. In the second alloy, the ratio of same elements is 4:7. If equal quantities of these two alloys the mixed to form a new alloy, then what will be the ratio of both of the pae elements in the new allloy?

a) 2:3 b) 16:35 c) 4:5 d) 40:59

21) In a mixture of 60L, the ratio of ethanol to ether is 4:1. The quantity of ether to be added to the mixture to make this ratio 2:1 will be 

a) 10L b) 12L c) 18L d) 24L 

22) The price of a variety of a commodity is Rs 5 per kg and that of another is Rs 8 per kg. The ratio in which two verities should be mixed, so that the price is Rs 7 per kg will be 

a) 1:2 b) 2:1 c) 3:1 d) 8:5

23) How many kilogram of rice costing Rs 18.30 per kg must be mixed with 126 kg of rice costing Rs 8.55 per kg so that 20% may be gained by selling the mixture at Rs 14.40 per kg ?

a) 55 kg b) 69 kg c) 84kg d) 75 kg

24) A container contains 40L of milk. 4 L of milk taken out and replaced by same amount of water from this container. This process was further repeated two times. How much milk is now there in the container?

a) 28L b) 27.16L c) 29.16 L d) 31.25 L

25) Two containers have milk and water in the ratio 2:1 and 3:1 respectively. If equal quantities of both containera are emptied into a bigger container, then find the ratio of milk to water in bigger container.

a) 5:1 b) 15:16 c) 6:5 d) 17:7

1d 2d 3a 4c 5a 6b 7a 8a 9c 10d 11b 12b 13c 14b 15a 16a 17d 18a 19b 20d 21b 22a 23b 24c 25d