EXERCISE -A
a) 60 paise & &1.35. 4:9
b) 4 months & 1 year 6 months. 2:9
c) 60cm & 2.4m. 1:4
d) 1.5kg & 600gms. 5:2
2) Which ratio is greater : 17:21 or 23:28? 23:28> 17:21
3) Arrange the following ratios in the ascending order:
A) 19:21, 13:15, 11:24. 11:24, 13:15 , 19:21
4) Arrange the following ratios in the ascending order:
7:12,11:16,13:18. 13:18, 11:16, 7:12
5) Which is Greater ratio (x + 4y)/(x + 5y) or (x + 5y)/(x +6y) ? (x + 5y)/(x +6y)
6) Find the following:
a) Duplicate ratio of 2√a : 3√b. 4a:9b
b) Triplicate ratio of 2x: 3y. 8x³:27y³
c) sub duplicate ratio of 16x²: 25y². 4x: 5y
d) sub-triplicate ratio of 27a³: 125b³. 3a: 5b
e) The reciprocal ratio of 9:11. 11:9
7) Compound ratio of
a) duplicate ratio of 5:6, the reciprocal ratio of 25:32 and sub-duplicate ratio of 81:64. 1:1
b) x: 3y and 2a : b/3. 2ax: yb
c) x²/2 : y²/3 and the duplicate ratio of 1/x : 1/y. 3:2
d) 3a: 4b and the sub-duplicate ratio of 4/9a² : 1/16b². 2:1
e) 2y²: 3x² and the triplicate ratio of x : y. 2x: 3y
f) duplicate ratio of 5:6, reciprocal ratio of 25:42 and the sub-triplicate ratio of 216:343. 1:1
8) a) If x: y be the sub-duplicate ratio of (x - a): (y - a), then find the value of xy/(x +y). a
b) If (3x -9):(5x+4) is the triplicate ratio of 3:4, find the value of x. 12
c) If A: B= 4:9 and B: C= 6:5, find A: C. 8: 15
d) If A: B= 3:4 and B: C= 6:5, find A: B:C. 9: 12:10
e) If A: B= 2:3 and B: C= 4:7, find A: B:C. 8: 12:21
f) If A: B= 1/4:1/5 and B: C= 1/7:1/6, find A: B:C. 15: 12:14
g) 3A =4 B = 6C, find A: B : C. 4:3:2
h) If (2x +5y): (5x -7y)= 5:3, Find x: y. 50:19
i) If (4x +3y): (6x +5y)= 11:17, Find x: y. 2:1
j) If a: b= 2:3 find (5a+ 8b): (6a - 7b). 49:9
k) if (6x² - 3y²):(x² + y²) is equal to 6: 25 find the value of x:y . 3:4
9)a) What number must be added to each term of the ratio 3:5 to make it 11: 12? 19
b) What same number should be added to both terms of 7:12 to get the ratio 2:3? 3
10) a) The ages of A and B are in the ratio 7:8. 6 years ago, their ages were in the ratio 5:6. Find their present ages. 21,24
b) A ratio is equal to 3:4. If its consequent is 144, what is its antecedent? 108
c) Two numbers are in the ratio 5: 7. If 8 is subtracted from each, the ratio becomes 3:5. Find the numbers. 20,28
d) What should be subtracted from each term of the ratio 4:9 so that it becomes 1:3. 3/2
e) Two numbers in the ratio 3:5. If 8 is added to each number, the ratio becomes 2:3. Find the numbers. 24,40
f) Find the number which bears the same ratio to 7/33 that 8/21 does to 4/9. 2/11
g) Work done by (x- 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio 3:10. Find the value of x. 6
h) the cost of production of radio set is ₹900, which is divided between material, labour and overheads in the ratio 3:4:2. Calculate the cost of material used in the radio set. 300
i) A sum of money is divided in the ratio of 3:5. If the larger part is ₹3125, find the smaller part. 1875
j) Divide ₹2600 among A, B and C in the ratio 1/2: 1/3: 1/4. 1200,800,600
k) when the fair of a certain journey by an airline was increased in the ratio 5:7, the cost of a ticket for the journey becomes ₹1421. Find the increase in the fare. 406
l) Sum of the two numbers is 38 and their difference is 2. What is the ratio between the numbers? 10:9
m) the ratio of the males to females in a committee of 48 members is 31. How many more ladies b added to the committee so that the ratio of the males to females may be 9:5 ? 8
n) a bav contains ₹142 in the form of Rs 1, 50 paise and 20 paise coins in the ratio of 3:5:8. Find the number of coins of each type. 60,100,160
o) A, B and C play cricket. The rund scored by A and B respectively are in the ratio 3:2. B's runs to C's runs are also in the ratio 3:2, and together they score 342 runs. How many runs did each score ? 162, 108, 72
p) Ages of two persons A and B are in the ratio 4:3. Five years hence the ratio of their ages will change to 9:7. Find their present ages. 40, 30yrs
q) In a mixture of 45 litres, the ratio milk to water is 13:2. How much water must be added to this mixture to make the ratio of milk to water as 3:1? 7 litres
r) In an examination, the ratio passes to failure was 4 :1. Had 30 less appeared and 20 less passed, the ratio of passes to failure would have been 5:1. How many students appeared for the examination ? 150
PROPORTION
EXERCISE-B
1) Find x, when
a) If x², 4 and 9 are in continued proportion. 4/3
b) 1:3:: x:7. 7/3
c) x: 1.5 ::3:5. 0.9
d) 2.5 :1.5:: x :3. 5
e) x: 50:: 3:2 . 75
2) Find the third proportional to:
a) 9, 6. 4
b) 8/3, 4. 6
c) 1.6, 2.4. 3.6
d) 0.24, 0.6. 1.2
e) (2 + √3),(5 + 4√3). (26+7√3)
f) [a/b + b/a] and √(a²+b²). ab
3) Find the fourth proportional to:
a) 3, 12 and 15. 60
b) 1.4, 3.2 and 7. 16
c) 1.5, 4.5 and 3.6. 10.8
d) (a²- ab +b²),(a³+ b³) and (a - b). a²- b²
4) Find the mean proportion of :
a) 5 and 80. 20
b) 2.5 and 0.9. 1.5
c) 1/12 and 1/75. 1/30
d) (8 - 4√3) and (6 + 3√3). 2√3
5) a) What number should be subtracted from each of the following numbers 23, 30, 57 and 78 so that the reminders are in proportion ? 6
b) what least number must be adde to each of the number 16, 7, 79 and 43, so that the resulting numbers are in proportion ? 5
c) Find two numbers whose mean proportional is 16 and the third proportion is 128. 8,32
d) What number should be added to each of the number 12, 22, 42 and 72 so that the resulting number maybe proportion. 3
e) If (x - 2), (x + 2), (2x + 1) and (2x + 19) are in proportion, find the value of x. 4
f) if (x + 5) is the geometric mean between (x+ 2) and (x + 9), find the value of x. 7
5) If x/a = y/b = z/c then find the value of
6) a) [(a²x²+ b² y²+ c² z²)/(a³x + by³+ c³z)]³/² √(xyz/abc).
b) If a/b = c/d = e/f, then value of (a²+d² + f²)/(a²+ c² + e²) is. (ab + cd + ef)².
c) (a³+c³)²/(b³+ d³)². e⁶/f⁶
d) (pa³+qc³+ re³)/(pb³+ qd³+ rf³). ace/bdf
7) a, b, c, d are in continued proportion, find the value of
a) (a-b)³/(b-c)³. a/d
b) √(2a²+7b²)/√(2c²+ 7d²). (a+ b)/(c+ d)
EXERCISE- C
1) Find the value of a:b:: c: d from the following:
a) (4a+5b)(4c-5d) = (4a-5b)(4c+5d)
b) (pa+qb):(pc+qd) :: (pa-qb):(pc- qd)
c) (5a+6b)/(5c+6d)=(5a-6b)/(5c-6d).
d) (3a+4b)/(3c+4d)=(3a-4b)/(3c-4d).
e) (a+3b+2c+6d)/(a-3b+2c-6d) = (a+3b-2c- 6d)/(a-3b-2c+6d)
f) (a+b+c+d):(a+b-c-d) :: (a-b+c- d):(a-b-c+d).
g) (2a+2b-3c-3d)/(2a-2b-3c+3d) = (a+b- 4c- 4d)/(a-b-4c+4d).
h) If a: b:: c: d, Prove the following:
i) (2a+5b)/(2a-5b) = (2c+ 5d)/(2c-5d).
j) (5a+11b)/(5c+11d) = (5a-11b)(5c-11d)
k) (2a+3b)(2c-3d) = (2a-3b)(2c+3d)
l) (3a - 5b)/(3c+5d)=(3c- 5d)/(3c+ 5d)
m) (la+mb):(lc+ md) :: (la-mb): (lc- md).
2) a) If x= 2ab/(a + b) then find the value of (x+a)/(x -a) + (x+ b)/(x-b). 2
b) If x= 6ab/(a + b) then find the value of (x+3a)/(x -3a) + (x+ 3b)/(x- 3b). 2
c) If (x³+3x)/(3x²+1) = 341/91tnen find the value of x. 11
3) Find x from the following:
a) {√(2- x) + √(2+x)}/{√(2- x) - √(2+x)}= 3. -6/5
b) {√(1+ x) + √(1-x)}/{√(1+ x) - √(1- x)}= a/b. 2ab/(a²+ b²)
c) {√(a+ x) + √(a-x)}/{√(a+ x) - √(a- x)}= c/d. 2acd/(c²+ d²)
d) {√(x+4) + √(x -10)}/{√(x +4) - √(x -10)}= 5/2. 263/20
e) {(a- x)/(a+x)}³ =16{(a+ x)/(a-x)}. -a/3, -3a
f) (1+ x+ x²)/(1-x+ x²)=62(1+x)/63(1-x). 1/5
g) {√(x +5) + √(x -16)}/{√(x+5) - √(x -16)}= 7/3. 20
4) a) If {√(2a +1) + √(2a -1)}/{√(2a+1) - √(2a -1)}= x. Then find the value of x²- 4ax +1. 0
b) {√(b +3a) + √(b -3a)}/{√(b+3a) - √(b -3a)}= x, then find the value 3ax²- 2bx + 3a. 0.
c) {3√(m +1) + ³√(m -1)}/{³√(m+1) - ³√(m -1)}= x then find the value of x³- 3x²m+ 3x is m
d) {√(a +3b) + √(a -3b)}/{√(a+3b) - √(a -3b)}=x, then 3by²- 2ax is. 3b
Exercise -D
1) Find the third proportional to 15, 20.
2) Divide ₹1320 among 7 men, 11 women & 5 boys so that each women may have 3 times as much as a boy, and a man as much as a woman and a boy together. Find how much each person receives.
3) How many one rupees coins, fifty-paise coins & twenty-five paise coins of which the numbers are proportional to 5/1, 3 and 4 are together worth & 210 ?
4) In 40 litres mixture of milk and water in the ratio of milk and water is 3:1. How much water should be added in the mixture so that the ratio of milk to water becomes 2:1 ?
5) Side of a hexagon becomes 3 times. Find ratio of areas of new and old hexagons.
6) find the number which when added to the terms of the ratio 11: 23 makes it equal to the ratio 4:7.
7) the sum of two numbers is 84. if the two numbers are in the ratio 4:3, find the two numbers. 48, 36
8) if 4a = 3b, find (7a+9b):(4a+5b). 57: 32
9) the number of red balls and green balls in a bag are in the ratio 16:7. if there are 45 more red balls then green balls. find the number of green balls in the bag. 45
10) what least number must be added to each of a pair of numbers which are in the ratio 7:16 so that the ratio between the terms become 13:22 ? 6
11) A number is divided into four parts such that 4 times the first part, 3 times the second part, 6 times the third part and 8 times the fourth part are equal. In what ratio is the number divided? 6:8:4:3
12) Divide 3150 into four parts such that half of the first part, a third of the second part, a fourth of the third part is equal to one- twelfth of the fourth part. 300, 450, 600,1800.
13) if x: y= 4:3, y: z= 2:3, find x:y:z. 8:6:9
14) If a/b = 4/5, then find (2a²-3b)/(7a+6b²). Can't determined
15) Two numbers are in the ratio 4:5, if 7 is added to each, the ratio between the numbers becomes 5: 6. find the numbers. 28, 35
16) Find x: if x+2 : 4x+1 :: 5x+2 : 13x+1. 0 or 2.
17) The total monthly sales of two companies A and B are in the ratio 2:3 and their total monthly expenditures are in the ratio 3:4. Find the ratio of the profits of the two companies given that company A's profit is equal to a fifth of its sales. 6:13
18) If a: b= 3:7, what is the value of (4a+5b)/(2a+2b).
A) 47/20 B) 36/24 C) 56/32 D)10/4 E) none.
19) If a: b= 2:3, b: c= 4:3 , and If c: d= 2:3, find a: b: c: d.
A) 8:12:9:27 B) 16:24:18:27
C) 18:27:36:8 D) none
20) Vipin's present is twice what the age of Kishor was one year ago. What is the sum of their present ages (in years), if the ratio of the sum of their present ages to the difference of their present ages is 19:5?
A) 21 B) 19 C) 24 D) 34
21) The weight of the Bimal and Basu are in the ratio 2:3 and the weights of Basu and Bali are in the ratio 4:3. what is Basu's weight (in kg) if the sum of the weights of Bimal, Basu and Bali is 203 kgs ?
A) 84 B) 76 C) 49 D) 65 E) none
22) the ratio of the number of boys to the number of girls in school is 7:3. If an additional 15 girls were to join the class, the ratio of the number of boys to the number of girls would become 2:3. what is the initial number of the girls in the class ?
A) 4 B) 6 C) 12 D) 5 E) none
23) if k= (a+c)/(b+d) = (c+r)/(f+d) = (a+e)/(b+f) when all quantities are positive, then which of the following must be true ?
A) k= e/f B) k= a/b C) k= c/d D) All of the above E) none
24) if 3 is subtracted from the numerator and 5 is added to the denominator of a fraction, the new fraction formed is 1/2. if 2 is added to the numerator of the initial fraction, the ratio of the new numerator to the denominator becomes 1:1. find the original fraction.
A) 11/13 B) 18/23 C) 13/15 D) 5/14 E) none
25) The ratio of the Ahmed's age to Mohammad's age is the same as the ratio of the ages of their respective elder brothers. The ratio of the difference of the ages of the ages of Ahmed and Mohammad to that the difference of the ages of their respective brothers is 1:2. what is the ratio of the sum of the ages of their respective brothers to the sum of the ages of the Ahmed and Mohammad?
A) 2:1 B) 4:1 C) 3:1 D) √2:1
26) Three different types of balls priced at ₹5, ₹8 and ₹13 per piece are displayed in three different boxes by a trader. Mr Paul bought from this shop all three types of balls spending a total sum of ₹768. The numbers of the balls ihe bought, taken in the order in which the prices are mentioned above, are in the ratio 5:4:3. How many balls of the costliest veriety did he buy ?
A) 104 B) 64 C) 24 D) 72
27) the mean proportional between two numbers is 9 and third proportion of the two numbers is 243. find the larger of the two numbers.
A) 27 B) 81 C) 9 D) none
28) If 3x - 4y +2z= 0 and 4x - 2y-z= 0, find x:z: y.
A) 8:10:11 B) 8:11:40
C) 11:40:8 D) 8:40:11
29) A person with him a certain number of weighing stones of 100gms, 500 gms and 1kg in the ratio 3:5:1. If a maximum of 5 kg can be measured using weighing stones of 500 gms alone, then what is the number of 100 gm stones he has ?
A) 6 B) 3. C) 9 D) 5
30) What must be subtracted from p and added to q so that the ratio of the resultant becomes 1:3.
A)(p+q)/3 B) (3p-q)/4 C) (p-q)/(p+q) D) (q-3p)/4
31) p,q,r,s, n and m are positive integers such that 4p= 5q= 6r= 12s= 8n = 9m. Which of the following pairs contains a number, which is not integer?
A) {pq/54, (m+n)/17}
B) {q/9, (rs/p}
C) {(r-s)(n-m),(q+s)/17}
D) {p/m, m/q}
** the amount used to purchase one litre of petrol can be used to purchase 3 litres of diesel of 5 litres of kerosene. Out of certain amount, ₹510 is spent on diesel.
32) how much is spent on kerosene if equal volumes of the 3 liquids are purchased with the total amount ?
A) ₹300 B) ₹306 C) ₹382 D) ₹354
33) what will be the amount spent on petrol if the total amount referred in Q. 56 is spent to purchase equal volumes of petrol and kerosene only ?
A) 1250 B)1275 C)1955 D) 1360
34) some apples are divided among 4 people Karan, Kiran, Kumar and Khanna. the ratio of the number of apples given to Kiran to the total number of apples given to Karan and Khanna is 1:2. the ratio of the number of apples given to Kumar to that of the remaining apples is 2:5. Khanna gets 2 apples more than Kiran, Karan gets half the number of apples that Kumar get. What is the total number of apples distributed ?
A) 21 B) 18 C) 19 D) 24
35) If (2x²-4x+3)/(4x-3) =(2x²-3x+5)/(3x-5) Find the value/s of x.
A) 0 B) 2 C) -2 D) both A and C
36) A certain number is added to each of a pair of a numbers which are in the ratio 4:7. The sum of the resulting numbers is 75 and their ratio (taken in the same order as mentioned above) is 8:17. What is the number added ?
A) -12 B) 9 C) -13 D) 8
37) A garrison of 900 soldiers had food-stock sufficient for 30 days when the rate of consumption is 2.5 kg/day/soldier. After some days of consumption at the rate, 300 soldiers were transferred to another garrison and the balance food lasted for 25 days for the remaining soldiers. If the rate of consumption of the remaining soldiers was 3.0 kg/day/soldier, after how many days from the start, were the soldiers transferred?
A) 12 B) 10 C) 8 D) 15
38) Eight farmers take 4 hours to plough 12 acres of land. What is the area of land that will be ploughed, If 12 farmers work for 14 hours at the same efficiency as in the previous case ?
A) 52 acres B) 63 acres D) 58 acres D) 65 acres
39) Divide 66 into three parts such that the sum of the first two parts equals the third part and the second part is 3 less than twice the first part. What is the ratio of the parts are arranged in the ascending order ?
A) 14:17:19 B) 5:9:11 C) 11:7:4 D) 4:7:11
40) The speed of a locomotive without any wagons attached to it is 40 kmph. It diminishes by a quantity which is the proportional to the cube root of the number of wagons attached. if the speed of the locomotive is 34 kmph when 27 Wagon are attached, what is the maximum number of wagons that can be attached if the condition is that speed should not be fall below 30 kmph ?
A) 64 B) 125 C) 216 D) 343
41) A certain amount of money is divided among nine brothers. The second brother gets ₹2 more than twice the amount given to the first brother. the third brother gets ₹3 more than the thrice the amount given to the first brother, and so on till the ninth brother. If the ratio of the amount with the ninth brother to the amount with the first brother is 10:1, how much did the fifth brother get (in rupees)?
A) 100 B) 50 C) 90 D) 75
42) Manoj and Shiva, who are colleageues in an office, have their monthly savings in the ratio 2:3. Manoj spends two-thirds of his income every month. if the ratio of their monthly income is 3:4, what is the ratio of their expenditures?
A) 3:2 B) 4:5 C) 4:3 D) 5:3
** A test of 60 minutes contains questions on mathematics and English only. the time taken to solve a mathematics question is twice the time taken to answer an English question and the ratio of time taken to solve the mathematics questions to time taken to answer all English questions is 8/7.
43) what is the ratio of the number of English Questions to that of mathematics ?
A) 11/7 B) 7/4 C) 9/4 D) 7/5
44) if the total number of questions is 22. how many English questions can be answered in 18 minutes ?
A) 8 B) 10 C) 11 D) 9
Miscellaneous -1
1) If a: b = 5:3, find (5a+ 8b): (6a - 7b). 49:9
2) Two numbers are in the ratio 3:5. If 8 is added to each number, the ratio becomes 2:3. Find the numbers. 24,40
3) The cost of production of a radio set is Rs900, which is divided between material, labour and overheads in the ratio 3:4:2. Find the cost of material used in the radio set. Rs300
4) Find the ratio between 1.5kg and 600gm. 5:2
5) Arrange the following ratios in the ascending order:
19:21; 13:15; 11:24.
6) Arrange the following ratios in the descending order
7:12; 11:16; 13:18
7) If A: B= 4:9 and B: C= 6:5, find A: C. 8:15
8) If A: B= 3:4 and B: C= 6:5, find A: B: C. 9:12: 14
9) If A: B= 1/4: 1/5 and B: C= 1/7: 1/6, find A: B: C. 15::12::14
10) If 3A: 4B: 6C, find A: B: C. 4:3:2
11) What number must be added to each term of the ratio 3:5 to make it 11:12? 19
12) The ages of A and B are in the ratio 7:8, six years ago, their ages were in the ratio 5:6. Find their present ages. 21,24 years
13) A ratio is equal to 3:4. If its consequent is 144, what is its anticedent? 108
14) Find the number which bears the same ratio to 7/33 that 8/21 does to 4/9. 2/11
15) A sum of money is divided in the ratio of 3:5, if the larger part is Rs 3125, find the smaller part. Rs1875
16) Divide Rd2600 among A, B, C in the ratio 1/2, 1/3, 1/4. 1200, 800, 600
17) Sum of two numbers is 38 and their difference is 2. What is the ratio between the numbers. 10:9
