SIGNIFICANT FIGURES
P-1
1) How many significant figures of following:
a) 6.34. 3
b) 8.0614. 5
c) 19.40506. 7
d) 7.00. 3
e) 4.300. 4
f) 6.0 x 10⁸. 2
g) 9.12 x 10⁻⁶. 3
h) 0.0036. 2
i) 0.0002057. 4
2) Write the value of:
a) 3.6047 correct to four significant figures. 3.605
b) 9.0614 correct to two significant figures. 9.1
c) 16.7246 correct to three significant figures. 16.7
d) 0.002763 correct to two significant figures. 0.0028
3) Find the value of √3 correct to two decimal places. 1.73
4) Find the value of √3 correct to two decimal places. Use this value to evaluate 4√3 correct to two significant figures. 2.3
5) By rationalizing the denominator, find the value of 4/(7 - √5) correct to two significant figures , it being given that √5= 2.2361. 0.84
LINEAR EQUATIONS
P-1
1) 9x -7= 6x + 14. 7
2) (1- x)/6 + 2x/3 = (1- 7x)/4 + 13/6. 1
3) (6x -7)/(3x +1) = (2x +1)/(x +5) . 2
4) 2+ (2x -3)/(2x +3) = (3x +4)/(x +2) . -3
5) (2x +1)/10 - (x -2)/6 = (3- 2x)/15. Find y when 1/x + 1/y = 2. -7/5, 7/19
6) If m= (1- 3x)/5, n = (1- 2x)/3 and 3(n - 2m)+ 1=0, find the value of x. -1/2
PROBLEM ON LINEAR EQUATIONS
P-1
1) A number decreased by 8% of itself gives 115. Find the number. 125
2) One-fourth of a number exceeds one-fifth of Its succeeding number by 4. Find the number. 84
3) The sum of three consecutive positive even integers is 18 more than twice the smallest. Find the integers. 12,14,16
4) A two digit number is such that ten's digit exceeds twice the unit's digit by 2 and the number obtained by interchanging the digits is 5 more than 3 times the sum of the digits. Find the number. 83
5) The sum of two numbers is 77. When the larger number is divided by the smaller one, we get 3 as quotient and 5 as reminder. Find the numbers. 59
6) The denominator of a fraction is 4 more than its numerator. On substracting 1 from its numerator and adding 3 to its denominator, it becomes 1/3. Find the fraction. 5/9
7) Five years ago, a man was seven times as old as his daughter. Five years hence, the man will be three times as old as his daughter daughter. Find their present ages. 10,40
8) The ages of A and B are in the ratio 7:5. Ten years, hence, the ratio of their ages will be 9:7. Find their present ages. 35,25
9) The perimeter of a rectangular plot of land is 90m. If its length is increased by 2 m and breadth decreased by 3m, then its area is decreased by 41m². Find the original length and breadth of the plot. 20,25
10) The cost of a carpet 10m long is Rs 1600. If its breadth were 2m less, the cost would have been Rs 1200. Find the original breadth of the carpet. 8m
11) By selling a bicycle for Rs 1885, a man gains 16%. At what price did he buy the bicycle. Rs 1625
12) If a man drives his scooter at 40 km per hour, he reaches his destination 6 minutes too late and if he drives it at 60 km per hour, he reaches his destination 6 minutes too soon. How far is his destination. 24km
13) A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at an average speed of 4 kmph and partly on bicycle at an average speed 9 kmph. Find the distance travelled by him on foot. 16km
14) A boat travels 40 km upstream in a river in the same period of time as it takes to travel 50 km downstream. If the rate of stream be 2 kmph, find the speed of the boat in still water. 18 kmph
15) A and B together can do a piece of work in 8 days, which A alone can do in 12 days. In how many days can B alone do the same work ? 24 days.
16) The monthly incomes of Muskan and Rahul are in the ratio 5: 4 and their monthly expenditure are in the ratio 3:2. If each saves Rs 1600 per month, find their monthly incomes. 4000,3200
17) A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be mixed to make 10 litres of a 40% acid solution? 6
18) There are some benches in a class room. If 4 students sit on each bench, then 3 benches are left unoccupied. However, if 3 students sit on each bench, 3 students are left standing. How many students are there in the class? 48
GRAPH (LINEAR EQUATIONS)
P-1
1) Draw the graph of 3x + 2y =11. From the graph, find the value of y, when x= 2. 2.5
2) Draw the graph of 4x -3y +12=0 and use it to find the area of the triangle formed by the line and the Co-ordinate axes. 6 sq.units,
3) Draw a graph, using the adjoining table. Using the graph, find the values of a and b. State the linear relation between x and y.
x: 0 1 2 b
y: 1 3 a -3 5, -2
PERCENTAGE
P-1
1) Convert each of the following to a fraction:
a) 14%. 7/50
b) 50/3%. 1/6
c) 62.5%. 5/8
d) 1.8%. 9/500
2) Convert each of the following into a decimal:
a) 12% . 0.12
b) 27.5%. 0.275
c) 3.6%. 0.036
d) 0.8%. 0.008
3) Convert each of the following into a percentage:
a) 3/4. 75%
b) 9/40. 22.5%
c) 0.45. 45%
d) 1.063. 106.3%
4) Evaluate:
a) 18% of Rs 3500. Rs 630
b) 100/3% of 180 grams. 60 gm
5) What percentage of 72 is 12 ?
6) What percentage is 490gm of 1 kg 400 g ?
7) What percentage is 54 P of Rs 3 ?
8) What percentage is 60 ml of a litre ?
9) 60% of a certain number is 18.6. Find the number.
10) if 32% of the students in a school are girls and the number of boys in the school is 731. Calculate the total strength of the school.
11) A solution of salt and water contained 15% salt. After evaporating 30 kg of water from it, the remaining solution has 20% salt. Find the weight of the original solution.
12) In an election contested by two candidates , the winning candidate secured 57% of the total votes polled and won by a majority of 43456 votes. Calculate
a) the number of total votes polled.
b) the number of votes cast for the losing candidate.
13) Mr Jones gave 40% of the money he had, to his wife. He also give 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of Rs 12000 was deposited in the bank. How much money did Mr. Jones have initially ?
14) A student X secured 30% marks in an examination and failed by 15 marks. Another student Y secured 40% marks and obtained 35 marks more than those required to pass. Find the maximum marks and the pass percentage of marks.
15) If A's salary is 25% more than that of B, then how many percent is B's salary less than that of A ?
16) A reduction of 10% in the price of sugar, enables a man to buy 1 kg sugar more for Rs 162. Find
a) the original rate per kg.
b) the reduced rate per kg.
17) If the price of tea is raised by 20%, by how much percent must a housewife reduce her consumption of tea so as not to increase the expenditure of the family on tea ?
18) Robin spend 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. Find the percentage increase in his savings.
19) The length of rectangle is increased by 10% and its breadth is increased by 20%. Find the percentage increase in its area.
20) In an examination, 70% of the candidates passed in English, 65% in Mathematics and 27% failed in both the subjects. If 558 candidates passed in both the subjects , find the total number of candidates.
21) The cost of manufacturing an article is dividing between material and labour in the ratio 8: 7. if the cost of a material be increased by 40% and the cost of labour be decreased by 20%, find the resulting change percentage in the total cost.
22) The population of a town has been increasing at the rate of 6% per annum. It its present population is 19663, what was it 2 years ago?
23) A mechanic was purchase 3 years ago, its value depreciates at the rate of 10% per annum. If its present value is Rs 94770, for how much was it purchased ?
PROFIT, LOSS AND DISCOUNT
P-1
1) A man buys an article for Rs 78 and sells it for Rs 89.70. Find his profit percent.
2) A watch is bought Rs 875 and sold for Rs 717.50. Find the loss percent .
3) A shopkeeper buys goods worth Rs 1800 and sells them of a profit of 25%. If 30% of the income of deduced as tax, find profit his net profit and profit percentage.
4) A purse is bought for Rs 675. Find the selling price when it is sold:
a) at 8% profit.
b) at 6% loss.
5) By selling an article for Rs 34.40, a man gains 7.5%. What is its cost price ?
6) By selling an article for Rs 720, a man inurs a loss of 4%. At what price should he sell the article to gain 16% ?
7) A man bought lemons at 5 for Rs 4 and sell them at 6 for Rs 5. Find his gain or loss percent.
8) The cost price of 20 books is equal to the selling price of 16 books. Find the gain percent.
9) A TV and a VCR were sold for Rs 19800 each. The TV was sold at a loss of 10% whereas the VCE at a gain of 10%. Find the gain or loss percent in the whole transaction.
10) A bicycle was sold at a gain of 16%. Had it been sold for Rs 70 more, the gain would have been 20%. Find the cost price of the bicycle.
11) A men sold a briefcase at 8% profit. Had he purchased it for 10% less and sold it for Rs 72 less, he would have gained 50/3%. For how much did the man purchase the briefcase ?
12) Arun bought a watch and spent Rs 120 on its repairs . He then sold it to Ved at a profit of 20%. Ved sold it to Vinod at a loss of 10%. Vinod sold it for Rs 1782 at a profit of 10%. How much did Arun pay for the watch ?
13) Aman purchased 30 kg of rice at the rate of Rs 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs 18.60 per kg and made 20% overall profit. At what price per kg did he purchase the second lot of 30 kg rice ?
14) A trader mixes three varieties of groundnuts costing Rs 50, Rs 20 and Rs30 per kg in the ratio 2:4:3 in terms of weight, and sella the mixture at Rs 33 per kg. Find his profit percentage .
15) A business sold 2/3 of his stock at a gain of 20% and the rest at a gain of 14%. Find the overall percentage of gain to the businessmen.
16) The CP of two watches taken together is Rs 840. If by selling one at a profit of 16% and the other at a loss of 12%, there is no loss or again in the whole transaction, find the respective cost price of the two watches.
DISCOUNT
P-1
1) The marked price of a shirt is Rs 840 and the shopkeeper allows a discount of 15% on it. Find
a) the discount
b) the selling price.
2) A trader marks his good 35% above cost price and allows a discount of 20%. What gain percent does he make ?
3) A dealer allows a discount of 20% to his customer and still gains 20%. Find the marked price of an article which costs the dealer Rs 1500.
4) How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 15% on the marked price, he gains 19% ?
5) A trader buys goods at 19% off the list price. He wants to get a profit of 20% after allowing a discount of 10%. At what percent above the list price should he mark the goods ?
6) A shopkeeper sold an article offering a discount of 5% and earned a profit of 47/2%. What would have been the percentage of profit earned if no discount was offered ?
7) A trader mark ped his goods at 20% above the cost price. He sold half the stock at the marked price, one-quarter at a discount of 20% on the marked price and the rest at a discount a 40% in the marked price. Find his overall profit percentage.
8)A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8%. If the customer pays Rs 680.40 as the price including a sales tax, then what is the marked price of the item ?
9) Find the single discount equivalent to two successive discounts of 25% in 8%.
10) Which of the following discount series is better for a customer : 20%, 10% or 18%, 12% ?
11) The marked price of a watch was Rs 720. A man bought the same for Rs 550.80 after getting the two successive discounts, the first one being 10%. What was the second discount rate ?
12) The difference between a discount of 35% and two successive discount of 20% on a certain bill was Rs 22. Find the amount on the bill ?
SIMPLE INTEREST
P-1
1) Find the simple interest on:
a) Rs 2400 at 9% p.a for 5/2 years.
b) Rs 800 at 20/3% p.a for 9 months.
2) Find the simple interest on Rs 5500 18% at 7% p.a from March, 25 to August, 18 of a particular year.
3) What sum invested at 9% p.a will yield a simple interest of Rs 630 in 7 months ?
4) What sum will amount to Rs15250 in 2 years 9 months at 8% per annum simple interest ?
5) In what time would a sum of money amount to three times itself at 15% p.a simple interest ?
6) A sum of Rs800 amounts to Rs 920 in 3 years at simple interest. If the intrest rate to increase pd by 3%, it would amount to how much ?
7) At what rate percent p.a simple interest, would a sum double itself in 6 years?
8) Adam borrowed some money at the rate of 6% p.a for the first two years, at the rate of 9% p.a for the next years, and at the rate of 14% p.a for the period beyond 5 years. if he pays a total interest of Rs 11400 at the end of 9 years, how much money did he borrow ?
9) At a certain rate of simple intrest, a sum amounts to Rs 4760 in 3 years and Rs5600 in 5 years. Find the sum and the rate percent per annum.
10) A sum of Rs 30000 was lent at simple interest, partly at 12% p.a for 7/2 years and partly at 25/2% p.a for 4 years. If the total interest earned be Rs 13720, find the sum lent at each rate .
11) Divide Rs 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal , the rate of interest being 5% per annum at simple interest.
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