Aptitude Book

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Contents

Chapters Page Number

1. Percentage 02 - 07

2. Profit & loss 08 - 14

3. Ratio & Proportion and Variation 15 - 21

4. Partnership 22 - 29

5. Simple Interest & Compound Interest 30 - 38

6. Averages and Mixture & Alligation 39 - 45

7. Time & Work 46 - 52

8. Time Speed and Distance 53 - 60

9. Number System 61 - 76

10. Permutation and Combination 77 - 84

11. Probability 85 - 91

12. Set Theory

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CHAPTER 1

PERCENTAGES Percentage:

The word percentage means per hundred, for example, if a person saves of his income it means he saves 30

part for every 100 part he earns.

Ex. 1 : quantity of water in milk constitutes 5 parts every 15 parts of the mixture what is the percentage of

water in the mixture?

Solution:

Percentage of Water = No. of parts of water/No. of parts of mixture

= 5/15 x100=33.33%

Percentage increase or decrease is calculated with respect to the base value unless mentioned otherwise.

Percentage increase or decrease = increase or decrease/base value x 100

Ex. 2 : if As income is 25% more than Bs income then by what percentage is Bs income less than As?

Solution:

Let Bs income =100

As income =100+25% of 100=125

Bs income is less than As income by 25

Percentage decrease= decrease/base value x100

= 25/125x100=20%

Note here bs income is compared with As income, so As income should be taken as base value.

If a quantity is increased by x% then the final quantity is obtained by multiplying original quantity with

(100+x/100)

If a quantity is reduced by r%, then the final quantity is obtained by multiplying original

Quantity with (100+r/100)

Ex. 3 : if the price of petrol is increased by 20% and subsequently by 40% , what is the final price if the

original price is Rs. 25?

Solution:

Final price= original price x (100+a/100) x (100+b/100)

Therefore Final price = 25 x (100+25/100) x (100+40/100) = 42 Rs.

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Note: use negative sign in case of price reduction.

Successive increase or decrease of percentage:

Let a be the first percentage change and b be the second, the net change is given by [a+b+axb/100]%

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LEVEL 1

1) The population of a town has increased from 133575 to 138918. The percent increase in population is.

(A) 2.5% (B) 3.5% (c) 3% (D) 4%

2) Mr. Smith credits 20% of his salary into a fixed deposit account and spends 35% of the remaining on groceries, if cash in hand is Rs.2600 what is his salary?

(A) 4000 (B) 4500 (C) 5000 (D) 5500

3) The price of an article has been reduced by 30% , in order to restore the original price the current price must be increased by?

(A) 30% (B) 42 6/7% (C) 23 1/3% (D) 42 1/9%

4) If the denominator is increased by 20% and the numerator is diminished by 10% the value of fraction is 21/6, the original fraction is ?

(A) 5/4 (B) 7/4 (C) 4/7 (D) 14/3

5) If a number is increased by 12% and then decreased by 18%, then find the net % change in the number.

(A) 8.16% decrease (B) 8.42 % increase (C) 8.44% decrease (D) 8.18% increase

6) The price per Kg of rice increases by 20% by what percentage should the consumption be decreased such that expenditure remains the same?

(A) 20% (B) 16.67% (C) 25% (D) 16.33%

7) Daniel bought a calculator at the store with the tax of 7.5%.The tax amount was 187.Find the calculator price before tax?

(A)Rs.174 (B) Rs. 171 (C) Rs. 170 (D) Rs. 179

8) The value of a machine depreciates at the rate of 20% every year. It was purchased 2 years ago. If its present value is 6400, its purchase price was

(A) Rs.9240 (B) Rs.7920 (C) Rs.6400 (D) Rs.10000

9) A reduction of 12.5% in the price of a dining table brought down its price to Rs.4375, the original price (in Rs.) of the table was.`

(A) 5000 (B) 4900 (C) 5100 (D) None of These

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10) Avinash spends 30% of his income on scooter petrol, o the remaining on house rent and the balance on food. If he spends Rs.300 on petrol, then what is the expenditure on house rent?

(A) Rs.180 (B) Rs.175 (C) Rs.160 (D) Rs.165

LEVEL-2

1) In an examination, A got 10% marks less than B, B got 25% marks more than C and C got 20% less than D. If A got 360 marks out of 500, the percentage of marks obtained by D was:

(A) 85% (B) 74% (C) 82 (D) 80%

2) A rainy day occurs once in every 25 days. Half of the rainy days produce rainbows. The percentage of days having no rainbow is :

(A) 2% (B) 12.5% (C) 98% (D) 87.5%

3) 35.In an examination, 35% of total student failed in Hindi, 45% failed in English and 20% in both. The percentage of those who passed in both subjects is?

(A) 45% (B) 40% (C) 42.5% (D) 35%

4) A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

(A) 45% (B) 45 5 % (C) 54 6 % (D) 55%

5) Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

(A) 39, 30 (B) 41, 32 (C) 42, 33 (D) 43, 34

6) What percentage of numbers from 1to 70 have 1 or 9 in the unit's digit?

(A) 16% (B) 14% (C) 20% (D) 21%

7) In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate

got, was:

(A) 2700 (B) 2900 (C)3000 (D) 3100

8) Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

(A) Rs. 6876.10 (B) Rs. 6999.20 (C) Rs. 6654 (D) Rs. 7000

9) Two candidates fought an election. One of them got 84% of the total votes and won with 476 votes. What was the total number of votes polled ?

(A) 800 (B)7 00 (C) 550 (D) None of these

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10) In a test minimum passing percentage for girls and boys is 35% and 40% respectively. A boy

scored 483 marks and failed by 117 marks. What are the minimum passing marks for girls ?

(A) 425 (B) 525 (C) 500 (D) 450

11) A positive number is by mistake divided by 6 instead of being multiplied by 6. What is the %

error on the basis of correct answer?

(A) 3% (B) 97% (C) 17% (D) 83%

12) What 30% of a number is added to another number the second number is increases to its 140%.

The second number is =x% of the first number. The value of x is:

(A) 30% (B) 75% (C) 133.33% (D) 33.33%

13) In a class 52 students, 25% are rich and other are poor. There are 20 females in the class, of whom

55% are poor. How many rich males are there in the class ?

(A) 200 (B) 150 (C) 300 (D) data inadequate

14) Puneet scored 175 marks in a test and failed by 35 marks. If the passing percentage of the test is

35%, what are the maximum marks of the test ?

(A) 650 (B) 700 (C) 750 (D)600

15) 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%

COMPANY SPECIFIC QUESTIONS

1. If the radius of a circle is increased by 20% then the area is increased by:

(A) 44 % (B) 144 % (C) 120 (D) 40 % (Capgemini)

2. Which of the following is the greatest?

(A) 40% of 30 (B) 3/5 of 25 (C) 6.5% of 200 (D) five more than the square of 3

(Capgemini)

3. A number, when 35 is subtracted from it, reduces to its 80 percent. What is four-fifth of that number?

(A) 70 (B) 90 (C) 120 (D) 140 (L&T Infotech)

4. If 20% of A = B and 40% of B = C, then 60% of (A + B) is:

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(A) 30% of C (B) 60% of C (C) 75% of C (D) None of these (L&T Infotech)

5. A businessman sold 2/3 of his stock at a gain of 20% and the rest at a gain of 14%. The overall percentage of gain to the businessman is:

(A) 12% (B) 17% (C) 18% (D) 20% (Tata-Elxsi)

6. A candidate who gets 30% of the marks in a test fails by 50 marks. Another candidate who gets 320 marks fails by 30 marks. Find the maximum marks.

(A) 900 (B) 1000 (C) 1200 (D) 800 (PERSISTENT)

7. If 24% of 395 is y, then what is 360% of 79.

(A) y (B) 2y (C) 3y (D) 3.5 y (SAMSUNG)

8. A jogger wants to save 1/4th of his jogging time. He should increase his speed by how much percentage.

(A) 25% (B) 36.95% (C) 33.33 % (D) 43.73% (BirlaSoft)

9. A merchant gained 25% by selling a stock of grains. In maintaining the stock, he has spent 10,000 Rupees. If the total cost of grains sold is Rs. 60,000, how much has he gained?

(A) Rs. 5, 000 (B) Rs. 15,000 (C) Rs.10, 000 (D) None of these (ZENSAR)

10. In a class of 50 students, the score of 30% of students is above Shahrukh. What percent of students have score below Shahrukh?

(A) 70% (B) 68% (C) 66%s (D) None of these (ZENSAR)

ANSWER KEY LEVEL 1:

1 D 2 C 3 B 4 D 5 A 6 B 7 A 8 D 9 A 10 B

ANSWER KEY LEVEL 2:

1 D 2 C 3 B 4 B 5 C 6 C 7 A 8 A 9 B 10 B

11 B 12 B 13 D 14 D 15 A

ANSWER KEYCOMPANY SPECIFIC QUESTIONS:

1 A 2 B 3 D 4 D 5 C 6 B 7 C 8 A 9 A 10 B

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CHAPTER 2

PROFIT AND LOSS

1.1 Profit and Loss:

The difference between selling price and cost price is known as profit or loss.

Ex 1: Find the profit % , if an article worth 300% is sold for 312 ?

Solution:

Profit= selling price-cost price = 312 300 = 12

Profit % = profit / cost price x100

= 12 / 300 x 100 = 4%

Percentage reduction in consumption

If the rate of a commodity is increased, then the consumption should be reduced to maintain the same

expenditure.

Percentage reduction in consumption = (% change / 100% + change) x100

Profit = selling price cost price

Loss = cost price selling price

Profit % = profit / cost price x 100

Loss % = loss / cost price x 100

Selling price = [1 + gain% / 100] x cost price

Selling price = [1 + loss% / 100] x cost price

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Ex 2: If the rate of rice is increased by 25% then what should be the consumption to maintain the same

expenditure?

Solution:

= (25 / 100 + 25) x 100 = 20%

So the quantity of rice consumption should be reduced by 20% to maintain the same expenditure.

Successive Discount:

If two successive discounts of a% and b% are offered then the net discount offered is [a+b-axb/100]%

Ex 3: Find the net discount offered on two successive discounts of 20% and 30%?

Solution:

Net discount = [a + b a x b / 100]

= [20 + 30 20 x 30 / 100]

= 44 %

Discount is the reduction of price. if a% discount is offered then the article would be sold for (100 - a)% of

the cost price.

Selling price = (100-a) / 100 x Cost price

1.2 False Weight:

In case a false weight which is less than the actual weight is used then the transaction ends in a profit.

% profit = [error / true value error x 100]

Ex 4: If a shop keeper sells 800 gm at cost price claiming it to be 1 kg, find the gain %?

Solution:

% profit = [ error / true value error x 100]

= 200 / 1000 - 200 x 100 = 25%

In case where selling price of two articles is the same and one is sold at a loss of x% then after at a profit of

x% then this transaction always leads to a loss of x^2/100

1.3 Marked Price:

MRP of an article is known as Marked Price or labeled price or listed price and denoted by MP.

Discount always carried on MP (MRP). Marked Price is always 100 in the case of discount.

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LEVEL 1

1) A retailer buys 40 pens at the marked price of 35 pens from a wholesaler. If he sells these pens

giving a discount of 1%, what is the profit percent?

(A)13% (B) 10 % (C) 15 % (D) 16 %

2) John bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the

percentage of profit made by him?

(A) 55% (B) 60 % (C) 50 % (D) 36 %

3) A person incurs 5% loss by selling a bat for Rs 1140. At what price should the watch be sold to

earn 5% profit?

(A) 1260 (B) 1255 (C) 1270 (D) 1250

4) The price of an article including the sales tax is Rs 616.The rate of sales tax is 10%, if the

shopkeeper has made a profit of 12%, then the cost price of the article is?

(A) 490 (B) 530 (C) 500 (D) 600

5) Mayank Bothra purchased 20 dozens of toys at the rate of 375 Rs per dozen He sold each one of

them at the rate of Rs 33.What was his percentage profit?

(A) 5.6% (B) 4.8% (C) 6 % (D) 6.8%

6) A person earns 15% on investment but loses 10% on another investment .If the ratio of the two

investments be 3:5, what is the gain or loss on the two investments taken together?

(A) 65% (B) 55% (C) 60 % (D) 63%

7) An article costing Rs. 200 is marked 25% higher than its C.P. and is sold at a discount of 10% for

cash payment. A customer is ready to pay the complete money on the spot . What is the

shopkeepers percentage profit?

(A) 15% (B) 12.5% (C) 20 % (D) None of these

8) In a store a dress tagged at RS 800 was offered at a discount of 12.5% when it did not sell at owner

price an additional discount of 10%was offered .what was the final selling price?

(A) 630 (B) 650 (C) 550 (D) None of these

9 ) A man buys 5 horses and 7 bulls for Rs 1950 he sells the horses at a profit of 10%and bulls at a

profit of 16% and on the whole his gain is Rs 237 what price does he pay for a horse?

(A) 230 (B) 250 (C) 300 (D) 225

10) If a commission of 10% is given on the marked price of a book than the publisher gains 20%.If the

commission is increased to 15% than what is the gain percent?

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(A) 15 (B) 11.22 (C) 12.5 (D) 13.33

LEVEL 2

1) If toffees are bought at the rate 18 for a rupee than how many of them must be sold for a rupee to

gain 20%?

(A) 16 (B) 12 (C) 14 (D) 15

2) In order to increase revenue a dealer announces 20% reduction in the unit price of an article as a

result his sales volume increases by 20% .what is the overall gain / loss to the dealer?

(A) 5% loss (B) 8% loss (C) 4% loss (D) 8.5% loss

3) A dishonest dealer pretends to sell at the cost price but earn a profit of 25% by under weighing

.what weight must he be using for a kg?

(A) 700gm (B) 800gm (C) 750gm (D) 600gm

4) A man buys two goats at Rs. 120 each. He sells one at 25% gain and other at 25% loss. How much

is his profit or loss?

(A) No loss no gain (B) 1% Loss (C) 1% Profit (D) None of these.

5) Profit made by selling an article at Rs. 425 is the same as the loss incurred by selling it at RS. 375.

What is the cost price of the article?

(A) 500 (B) 400 (C) 600 (D) 550

6) A shopkeeper bought 22kg of certain commodity of type A at rate of Rs. 8.40 per kg and 28 kg

of the same commodity of type B at rate of Rs. 6.30 per kg. He mixed the two types and sold the

mixture at the rate of Rs 7.8 per kg. What is his profit or loss?

(A) 28.8 profit (B) 27 profit (C) 30 profit (D) 25 profit

7) A shopkeeper offers a discount of 15% after making up 70% on cost price. As a result ,his profit

drops by Rs. 127.5 .Find the cost price?

(A) Rs.500 (B) Rs. 450 (C) Rs.600 (D) Rs. 550

8) A person purchases 50 dozen eggs at Rs.4 per dozen. Of these, 40 eggs were found broken. At

what price should he sell the remaining eggs in order to make a profit of 5%?

(A) Rs. 5.00 (B) Rs. 4.50 (C) Rs. 6.50 (D) Rs. 4.00

9) Two articles sold at Rs. 198 each such that a profit of 10% is made on the first while a loss of 10%

is made on the other. What would be the net profit/loss on the two transactions combined?

(A) 27% (B) Rs. 4 (C) No change (D) None of these

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10) If the income of Ram is more than that of Shyam by 37.5%, then by how much % Shyams income

is less than that of Ram?

(A) 27% (B) 25% (C) No change (D) None of

these

11) If books bought at price ranging from Rs.200 to Rs.325 are sold at prices ranging from Rs.300 to

Rs.450, what is the greatest possible profit that might be made in selling eight books?

(A) Rs.400 (B) Rs. 2000 (C) Rs.600 (D) Cannot be determined

12) Saif purchased 20 dozens of toys at the rate of Rs.375 per dozen. He sold each one at the rate of

Rs.33. What was his percentage profit ?

(A) 3.5% (B) 5% (C) 5.6% (D) 6.5%

13) A sells an article which costs him Rs.500 to B at a profit of 20%. B then sells it to C, making a

profit of 10% on the price he paid to A. How much does C pay B ?

(A) Rs.472 (B) Rs.476 (C) Rs.528 (D) Rs.660

14) The profit earned by selling an article for Rs.832 is equal to the loss incurred when the same article

is sold for Rs.448. What should be the sale price for make 50% profit?

(A) Rs.920 (B) Rs.960 (C) Rs.1060 (D) Rs.1160

15) A man purchased a box full of pencils at the rate of 7 for Rs.9 and sold all at the rate of 8 for

Rs.11. In this transaction, he gained Rs.10. How many pencils did the box contain ?

(A) 100 (B) 112 (C) 114 (D) 115


1. A vendor sold two things at Rs.12 each, with one item at 25% profit and other at 20% loss. By

this transaction he made profit or loss and by how much? [L&T Infotech]

(A) loss 40% (B) loss 60% (C) profit 27% (D) loss 38%

2. A trader, frauds by 10% while buying and 10% while selling the same. What is the total gain he

obtained during the transaction? [COGNIZANT]

(A) 13% (B) 20% (C)10% (D) None of these

3. The prices of Gold suddenly rose from Rs. 3000 per gram to Rs. 3298 per gram. Mrs. Verma was lucky enough to buy 340 grams yesterday only. How much Mrs. Verma will gain if she sells the gold today?

[BIRLA SOFT] (A) Rs. 98260 (B) Rs. 101320 (C) Rs. 62880 (D) Rs.70520

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4. A man sold two cows for Rs. 210 at a total profit of 5%. He sold one cow at a loss of 10% and

another at a profit of 10%. What is the price of each cow (in Rs.)? [INFOSYS]

(A) 130 & 60 (B) 120 & 80 (C) 150 & 50 (D) None of these

5. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price

of the item is? [ TCS ]

(A) A decrease of 99% (B) No change (C) A decrease of 1% (D) An increase of 1%

6. A merchant sells an item at a 20 percent discount, but still makes a gross profit of 20 percent of

the cost. What percent of cost would be the gross profit on the item have been if it had been sold

without the discount? [HCL]

(A) 20% (B) 40% (C) 50% (D) 60%

7. Ravi's salary was reduced by 25%. Percentage increase to be effected to bring the salary to the

original level is: [WIPRO]

(A) 33.33% (B) 25% (C) 20% (D) 30%

8. The total population of a village is 5000. The number of males and females increases by 10% and

15%, respectively and consequently the population of the village becomes 5600. What was the

number of males in the village? [WIPRO]

(A) 2000 (B) 2500 (C) 3000 (D) 4000

9. A shopkeeper labels the price of article 15% above the cost price. If he allow Rs 51.20 discount on

an article of Rs 1024, find his profit percent. [ACCENTURE]

(A) 10% (B) 8% (C) 12% (D) 9.25%

10. The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is

sold for Rs. 448. What should be the sale price for making 50% profit? [L&T INFOTECH]

(A) Rs. 920 (B) Rs. 960 (C) Rs. 1060 (D) Rs. 1200

ANSWER KEY LEVEL 1:

1 B 2 C 3 A 4 C 5 A 6 D 7 B 8 A 9 B 10 D

ANSWER KEY LEVEL 2:

1 D 2 C 3 B 4 C 5 B 6 A 7 A 8 B 9 B 10 D

11 B 12 C 13 D 14 B 15 B


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1 B 2 D 3 B 4 C 5 C 6 C 7 A 8 C 9 D 10 B

CHAPTER 3

RATIO, PROPORTION & VARIATION

3.1 Ratio:

A ratio is a comparison of two numbers by division.

The ratio of a to b is expressed as follows:

a:b=

Here a is called antecedent and b is called a consequent

3.2 Proportion:

Proportion is the equality of two ratios.

E.g. 4/20= 1/5 is a proportion

If a, b, c, d are in proportion

Then =

Ad = cb

Product of extremes = Product of means

3.3 Properties of Proportion:

If a/b = c/d then,

Invertendo b / a = d / c

Alternendo a / c = b / d

Componendo (a+b) / b = (c+d) / d

Dividendo (a-b) / b = (c-d) / d

Componendo & Dividendo (a+b) / (a-b) = (c+d) / (c-d)

Here, a is the 1st proportional and b is the 2nd proportional

c is the 3rd proportional d is the 4th proportional

3.4 Duplicate Ratios:

Duplicate ratio of (a : b) is (a2 : b2).

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Sub-duplicate ratio of (a : b) is (a : b).

Triplicate ratio of (a : b) is (a3 : b3).

Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).

3.5 Continued Proportion:

Three quantities a, b, c are said to be in continued proportion.

If a:b=b:c=>b=ac

Here, b is called the mean proportional of a and c

E.g. The mean proportional of 0.32 and 0.02 is

X= 0.08

Third proportional of a and b is b/a

E.g. Find the third proportional of 16 and 24

X=24/16=36

LEVEL 1

1. The number of marbles with A and B are in the Ratio of 10:11. Which of the following cannot be a

possible number of marbles with A and B together?

(A) 189 (B) 210 (C) 231 (D) 153

2. Two numbers are in the ratio of 2:5. If the difference between these numbers is 24, then find the

sum of the numbers.

(A) 52 (B) 46 (C) 48 (D) None of these

3. If a:b :: 1:6 and b:c :: 5:7, then, a:b:c = ?

(A) 2:14:56 (B) 3: 25:46 (C) 5:30:42 (D) None of these

4. The sum of three numbers which are in ratio 5:7:13 is 1250. The difference between the greatest

number and the least number is

(A) 50 (B) 100 (C) 400 (D) 300

5. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed

respectively in their salaries, then what will be the new ratio of their salaries?

(A) 3:3:10 (B) 10:11:20 (C) 23:33:60 (D) cant be determined

6. A's money is to B's money as 4:5 and B's money is to C's money as 2:3. If A has Rs.800, C has

(A) Rs. 1000 (B) Rs. 1200 (C) Rs. 1500 (D) Rs. 2000

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7. The mean Proportional between two numbers is 9 and the third proportional of the two numbers is

243. Find the larger of the two numbers?

(A) 27 (B) 81 (C) 9 (D) 54

8. If 93 is divided into two parts such that thrice the first part and twice the second part are in the

ratio 25: 4. Find the first part?

(A) 60 (B) 75 (C) 50 (D) 70

9. The students in three classes are in the ratio 2:3:5. If 20 students are increased in each class, the

ratio changes to 4:5:7. The total number of students before the increase were :

(A) 100 (B) 90 (C)10 (D) none of these

10. What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the

remainders are proportional?

(A) 10 (B)5 (C) 7 (D) 2

LEVEL 2

1. The monthly Expenses of Peter on his bike is partly fixed and partly vary with number of

kilometers he travels in a month. If he travels 100 kms in a month his total car expenses will be Rs

3500. If he travels 200 kms in a month, his total expenses will be Rs 4000. If he travels 500 kms in

a month, what will be his total expenses?

(A) 5500 (B) 5200 (C) 5300 (D) 5450

2. Three friends divide Rs.624 among themselves in the ratio 1/2:1/3:1/4. The share of the third

friend is :

(A) Rs. 288 (B) Rs.192 (C) Rs. 148 (D) Rs. 144

3. The ratio of flow of water in pipes varies inversely as the square of the radius of the pipes. What is

the ratio of the rates of flow in two pipes of diameters 2 cm and 4 cm?

(A) 3:1 (B) 6:1 (C) 7:15 (D) 4:1

4. Rs. 170 is generated using a combination of 10 paise, 25 paise and 50paise coins, if the ratio of

10paise, 25 paise and 50 paise coins is 5:10:11, then the total number of coins is:

(A) 100 (B) 200 (C) 520 (D) 220

5. A, B and C do a work in 20, 25 and 30 days, respectively. They undertook to finish the work

together for Rs.2220, then the share of A exceeds that of B by :

(A) Rs. 120 (B) Rs.180 (C) Rs.300 (D) Rs. 600

6. The ratio of the age of a man and his wife is 4:3. After 4 years, this ratio will be 9:7. If at the time

of marriage, the ratio was 5:3, then how many years ago they were married?

(A) 12 years (B) 8 years (C) 10 years (D) 15 years

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7. A, B, C and D share a property worth Rs. 77500.If A:B = 3:2,B:C = 5:4 and C:D=3:7. Find the

share of B.

(A) Rs. 20000 (B) Rs.15000 (C) Rs. 25000 (D) Rs. 22000

8. 243 have been divided into three parts such that half of the first part, one third of the second part

and one fourth of the third part are equal. The largest part is:

(A) 102 (B) 108 (C) 100 (D) 110

9. The proportion of milk and water in two samples is 5:2 and 7:5 if a mixture comprising of equal

quantities of two samples is made, the proportion of milk and water in the mixture is

(A) 12:7 (B) 7:12 (C) 109:59 (D) 59:109

10. The annual salary of Mr. John, Mr. Adam and Mr. Joe is in the ratio 2:3:5. If the salary of Mr. Joe

is 90,000 more than that of Mr. John, then the monthly salary of Mr. Adam is

(A) 7,500 (B)75,000 (C) 90,000 (D) None of these

11. If the work done by (x 1) men in (x + 1) days is to the work done by (x + 2) men in ( x 1) days

is in the ratio 9 : 10, then the value of x is

(A) 10 (B) 12 (C) 8 (D) 15

12. The duration of a railway journey varies as the distance and inversely as the velocity; the velocity

varies directly as the square root of the quantity of coal used, and inversely as the number carriages

in the train. In a journey of 50 km in half an hour with 18 carriages, 100 kg of coal is required.

How much coal will be consumed in a journey of 42 km in 28 minutes with 16 carriages?

(A) 64 kg (B) 49 kg (C) 25 kg (D) 36 kg

13. The weight of a circular disc varies as the square of the radius when the thickness remains the

same; it also varies as the thickness when the radius remains the same. Two discs have their

thicknesses in the ratio of 9: 8; the ratio of the radii if the weight of the first is twice that of the

second is

(A) 4 : 3 (B) 5 : 2 (C) 2 : 1 (D) 1 : 2

14. If a and b are positive integers then always lies between:

(A) (a + b)/( a b) and ab (B) a/ b and (a + 2b)/( a + b)

(C) a and b (D) ab/( a + b) and (a b)/ ab

15. The cost of digging a pit was Rs 1,347. How much will it cost (approximately) if the wages of

workmen per day had been increased by 1/ 8 of the former wages and length of the working day

increased by 1/ 20 of the former period?

(A) Rs 1443 (B) Rs 1234 (C) Rs 1439 (D) Rs 1000


17

1. The ratio of daily wages of two workers is 4:3 and one gets daily Rs. 9 more than the other. What

are their daily wages? [ACCENTURE]

(A) Rs. 32 and Rs.24 (B) Rs.60 and Rs. 45 (C) Rs. 80 and Rs. 60 (D) None of these

2. In a business P and Q invested amounts in the ratio 3:4, whereas the ratio between amounts

invested by P and R was 6:7. If Rs 106501.50 was their profit, how much amount did Q receive?

[ACCENTURE]

(A) Rs. 40572 (B) Rs 30429 (C) Rs 35500.50 (D) Rs 34629

3. If Rs. 1260 is divided amongst A, B and C in the ratio 2:3:4. What is Cs share?

[TCS]

(A) 850 (B) 560 (C) 620 (D) 460

4. The ratio of incomes of C and D is 3:4. The ratio of their expenditures is 4:5. Find the ratio of their

savings if the savings of C is one fourths of his income? [TCS]

(A) 13/17 (B) 8/11 (C)12/19 (D) None of these

5. If and , find the value of [ACCENTURE]

(A) 3/5 (B) 3/17 (C) 9/25 (D) 8/17

6. The ratio of boys and girls in a school is 370:356, and that of teachers to boys is 105:37. If the

number of girls in school is 6764, how many teachers are there in the school? [SAMSUNG]

(A) 6764 (B) 19950 (C) 20292 (D) 20342

7. The age of Ram and Sam are in the ratio 5:6 and after 4 years their ratios are 7:8 then what is the

present age of Sam? [TCS]

(A) 13 yrs. (B) 12 yrs. (C) 11 yrs. (D) none of these

8. 729 ml of a mixture contains milk and water in ratio 7:2. How much of the water is to be

added to get a new mixture containing half milk and half water? [HCL]

(A) 79 ml (B) 81 ml (C) 72 ml (D) 91 ml

9. Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should b e mixed, so that the resulting solution has 1 part milk and 2 parts water?

[COGNIZANT]

(A) 35:3 (B) 21:36 (C) Not possible (D) none of these

10. The sides of a triangle are in the ratio (1/2):(1/3):(1/4) and its perimeter is 104 cm. The length of the longest side is: [L & T ]

(A) 48 (B) 52 (C) 32 (D) 36

18

ANSWER KEY LEVEL 1:

1 D 2 D 3 C 4 C 5 C 6 C 7 A 8 B 9 A 10 D

ANSWER KEY LEVEL 2:

1 A 2 D 3 D 4 C 5 B 6 A 7 B 8 B 9 C 10 C

11 C 12 A 13 A 14 B 15 A

ANSWER KEY : COMPANY SPECIFIC QUESTIONS:

1 D 2 A 3 B 4 C 5 D 6 B 7 B 8 B 9 C 10 A

19

Chapter 4

PARTNERSHIP

4.1 Partnership

If two or more people jointly run a business, the profit or loss is shared in the ratio of the investments

done by the people involved. They are called partners and the deal is known as partnership. In short,

Partnership is an association of two or more parties, for a common business.

4.2 Types of Partnership

Partnership is of two types:

Simple Partnership: Simple partnership is the one in which the capitals of each of the partners are

invested for the same time and profit or loss in a partnership are divided among the partners in the

ratio of their investments.

Suppose A and B invest Rs. X and Rs. Y, respectively, for a year in a business, then at the end of the

year:

(A's share of profit): (B's share of profit) = x : y.

Compound Partnership: Compound partnership is one wherein the periods of investment are unequal.

And equivalent capital for a unit of time is calculated by multiplying the capital with the number of

time units it was in business.

Suppose A invests Rs. x for p months and B invests Rs. y for q months then,

(A's share of profit) : (B's share of profit)= xp : yq.

A partner who manages the business is known as a working partner and the one who simply

invests the money is a sleeping partner.

Ex. Three partners A, B and C invested Rs. 1000, Rs. 1200 and Rs. 1500 respectively in business for one

year. How should they divide a profit of Rs. 1295?

Solution: As investment period is same so, profit should be divided in ratio of capitals as, 10 : 12 : 15, also

10 + 12 + 15 = 37

Ex. A, B and C enter into a business. A put Rs. 1000 for 6 months, B puts Rs. 1200 for 8 months and C

puts Rs. 1400 for 10 months. Their gain was Rs. 666. Find out the share of each partner.

Solution: Ratio of profits will be 10*6 : 12*8 : 14*10 = 60 : 96 : 140 = 15 : 24 : 35

20

Ex. Three friends Ram, Shyam and Mohan enter into partnership. Ram put one forth of capital for one

fourth of the time. Shyam puts one third of capital for one half of time. Shyam puts remaining capital for

full period of time. Find the division of profit Rs. 806 among three friends.

Solution: Ram's share : Shyam's share : Mohan's share =

Now LCM of 16, 6, 12 is 48, so multiplying the equation by 48 we get ratio as 3 : 8 : 20 , also 3 +8 + 20 =

31

Ex. A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A

withdraws half of his capital and after 10 months, a profit of Rs 378 is divided among them. What is B's

share?

Solution : Ratio of investments =1/2 : 1/3 : 1/4 , now LCM of 2, 3, 4 is 12 on multiplying the ratio with 12

we get 6 : 4 : 3 , also we assume their initial investment be 6x, 2x and 3x so, we can write: A : B :C

Ex. A and B are partners in a business. A contributes 1 / 4 of the capital for 15 months and B received 2 / 3

of the profit, for how long B's money was used?

Solution : Let total profit is x

Let total capital invested be Rs P and A's money was used for 15 months while B's money was used for b

21

months then we can write the equation as-

So, B's money was used for 10 months

Ex. A began a business with Rs. 21, 000 and is joined afterwards by B with Rs. 42,500. For how much

period does B join, If the profits at the end of the year are divided in the ratio 3 : 1?

Solution: Let B joined for P months

then we can write equation as - (85,000 * 12 ) : ( 42,500 * P ) = 3 : 1

Ex. In a business A and C invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested

by A and B was 3 : 2 . If Rs. 56,914 was their profit, how much amount did B receive?

Solution : A : B = 3 : 2 , A : C = 2 : 1

B : A = 2 : 3 , B : A = 4 : 6

Now, A : C = 2 : 1, A : C = 6 : 3 , So B : A : C = 4 : 6 : 3

We can write as A : B : C = 6 : 4 : 3

LEVEL 1

1. Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of year both of them share the profits at the ratio of 2:1. After how many months Monty

joined Raj ?

(A) 4 Months (B) 8 Months (C) 5 Months (D) 6 Months

2. A and B started a business by investing money in ratio of 5:6. C joined them after few months by

sharing an amount equal to B's share. At the end of year 20% profit was earned which was equal to

Rs 98,000. How much money was invested by C?

(A) Rs 200000 (B) 210000 (C) 205000 (D) 215000

22

3. A, B and C shared profits in ratio of 5:7:8. They partnered for 14 months, 8 months and 7 months

respectively. What was the ratio of their investments?

(A) 21:49:56 (B) 20:49:56 (C) 20:49:64 (D) 24:49:64

4. X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they

make a profit of Rs.26400. What is the share of X in the profit?

(A) Rs.14400 (B) Rs.26400 (C) Rs.12000 (D) Rs.12500

5. A, B and C enter into a partnership investing Rs 35000, Rs 45000 and 55000. Find the their

respective shares in annual profit of 40,500

(A) 10500, 13500, 19500 (B) 10500, 13500, 18500

(C) 10500, 13500, 17500 (D) 10500, 13500, 16500

6. A, B and C start a business each investing Rs. 20,000. After 5 months A withdrew Rs. 5000, B

withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900

was recorded. Find the share of A?

(A) 21200 (B) 28200 (C) 20500 (D) 26000

7. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then

after six months with an amount equal to that of B. In what proportion should the profit at the end

of one year be distributed among A, B and C?

(A) 3 : 5 : 2 (B) 3 : 5 : 5 (C) 6 : 10 : 5 (D) Data inadequate

8. Sumit and Ravi started a business by investing Rs 85000 and 15000 respectively. In what ratio the

profit earned after 2 years be divided between Sumit and Ravi respectively?

(A) 17:1 (B) 17:2 (C) 17:3 (D)17:4

9. A,B and C enter into a partnership investing Rs 35000, Rs 45000 and 55000. Find the their

respective shares in annual profit of 40,500

(A) 10500, 13500, 19500 (C) 10500, 13500, 18500

(B) 10500, 13500, 17500 (D) 10500, 13500, 16500

10. Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C.

Then C's share is

(A) Rs 200 (B) Rs 300 (C) Rs 400 (D) Rs 500

LEVEL 2

23

1. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them

after six months with an amount equal to that of B. In what proportion should the profit at the end

of one year be distributed amount A, B and C

(A) 3:7:5 (B) 6:10:5 (C) 6:10:7 (D) 6:7:5

2. Three partners A,B and C shared the profit in a software business in the ratio 5:7:8. They had

partnered for 14 months, 8 months and 7 months respectively. Find the ratio of their investments?

(A) 19:49:64 (B) 20:49:64 (C) 20:49:65 (D) 20:50:64

3. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the

profit is divided in the ratio 2:3. What is B's contribution in the capital?

(A) Rs 9000 (B) Rs 7000 (C) Rs 5000 (D) Rs 4000

4. Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a

total profit of Rs. 13,800. Deepak's share is

(A) Rs 9600 (B) Rs 8500 (C) Rs 8450 (D) Rs 8400

5. A and B enter in to a partnership and A invests Rs.10, 000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If

B invests a certain sum in the partnership at the beginning of the year and leaves it intact and

receives Rs.9600 as his share of the total profit of Rs.19, 100 for the year, how much did B invest

in the company?

(A) Rs. 12000 (B) Rs. 96000 (C) Rs. 8000 (D) Rs. 6000

6. A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and ,Rs.1,50,000

respectively. Find the share of each, out of an annual profit of Rs. 56,700?

(A) Rs. 16800, 18900, 21000 (B) Rs. 16800, 21000, 18900

(C) Rs. 18900, 16800, 21000 (D) Rs. 18900, 21000, 16800

7. Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of

the year, they made a profit of Rs. 16,500. Find the lire of each.

(A) Rs. 3300, 6600, 3300 (B) Rs. 3300, 6600, 6600

(C) Rs. 6600, 6600, 3300 (D) Rs. 6600, 3300, 3300

8. A, B and C start a business each investing Rs 20,000 After 5 months A withdrew Rs.6000 B

withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900

was recorded. Find the share of each?

(A) Rs. 28200, 21200, 20500 (B) Rs. 20500, 28200, 21200

(C) Rs. 21200, 20500, 28200 (D) Rs. 20500, 21200, 28200

9. A, B and C enter into partnership, A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B?

(A) Rs. 1500 (B) Rs. 1200 (C) Rs. 1000 (D) Rs. 800

24

10. Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for

4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, find the total rent of the

field?

(A) Rs. 3000 (B) Rs. 3250 (C) Rs. 3500 (D) Rs. 3750

11. Nirmal and Kapil started a business investing Rs 9, 000 and Rs 12, 000 respectively. After 6

months, Kapil withdrew half of his investment. If after a year, the total profit was Rs 4, 600 what

was Kapils share in it?

(A) Rs. 2000 (B) Rs. 2600 (C) Rs. 1900 (D) Rs. 2300

12. A, B and C enter into a partnership investing Rs. 3800, Rs. 4200 and Rs. 4000, resp. A profit of

Rs. 1800 is divided among them. So what is the share of B?

(A) Rs. 520 (B) Rs.780 (C) Rs. 600 (D) Rs. 630

13. A started a business with a capital of Rs. 10000 and 4 month later, B joined him with a capital of

Rs. 5000.What is the share of A in the total profit of Rs. 2000 at the end of the year?

(A) Rs. 1500 (B) Rs. 1800 (C) Rs. 1600 (D) Rs. 1700

14. A, B and C start a business. A invests 3 times as much as B invests and B invests 2/3 of what C

invests. If the total profit is Rs. 1320, find the share of A.

(A) Rs. 720 (B) Rs. 620 (C) Rs. 600 (D) Rs. 800

15. B is a sleeping partner and A is the working partner. A puts in Rs. 5000 and B puts in Rs. 6000. A

received 12 % of profit for managing the business and the rest is divided in proportion to their

capitals. What is the share of A in a profit of Rs. 880?

(A) Rs. 770 (B) Rs. 460 (C) Rs. 520 (D) None of these

COMPANY SPECIFIC QUESTIONS 1. In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3

of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, Bs share is: [L & T]

(A) Rs. 650 (B) Rs. 800 (C) Rs. 960 (D) Rs. 100

2. Ram and Shyam invested Rs 3000 and Rs 4000 respectively in a business. If Ram doubles his

capital after 6 months, then in what proportion should Ram and Shyam divide that Years profit?

[WIPRO]

25

(A) 3:4 (B) 4:3 (C) 16:9 (D) 9:8

3. P started a business by investing Rs 2,700 after sometime Q joined him by investing Rs 2,025. At

the end of one year, the profit was divided in the ratio 2:1 After how many months did Q joined the

business? [TCS]

(A) 3 (B) 4 (C) 6 (D) 9

4. A, B and C are partners. A receives 2/3 of the preofit, B and C divide the remainder equally. As

income increased by Rs 400 when the rate of profit rises from 5 to 7 percent. The capital of B is?

[VEDANTA]

(A) Rs 30,000 (B) Rs 5,000 (C) 6,000 (D) 15,000

ANSWER KEY LEVEL 1:

1 A 2 B 3 C 4 A 5 D 6 C 7 C 8 C 9 D 10 C

ANSWER KEY LEVEL 2:

1 B 2 B 3 A 4 D 5 C 6 A 7 C 8 D 9 B 10 B

11 D 12 D 13 A 14 A 15 B

ANSWER KEY COMPANY SPECIFIC QUESTIONS:

1 B 2 D 3 B 4 B 5 6 7 8 9 10

Chapter 5

SIMPLE INTEREST COMPOUND INTEREST

The lending and borrowing of money has been happening since thousands of years. Any sum of

money, borrowed for a certain period, will invite an extra cost to be paid on the money borrowed;

this extra cost at a fixed rate is called the interest. The money borrowed is called the principal.

The sum of interest and principal is called the amount. The time for which money is borrowed is

called the period.

Amount = Principal + Interest

26

The interest paid per hundred (or percent) for a year is called the rate percent per annum. The rate

of interest is almost always taken as per annum; in calculations we will always consider it per

annum unless indicated.

The interest is of two types; one is simple, the other is compound.

5.1 Simple Interest (S.I)

It is the interest paid as it falls due, at the end of decided period (yearly, half yearly or quarterly),

the principal is said to be lent or borrowed at simple interest.

Simple Interest, SI = PRT / 100

Here P = Principal, R = Rate per annum, T = Time in years.

Therefore Amount, A = P + = P [1 + ]

If T is given in months, since rate is per annum, the time has to be converted in years, so the

period in months has to be divided by 12. If T = 2 months = 2/12 years

E.g. 1: Find the amount on S.I., when Rs. 4000 is lent at 5 % p.a. for 5 years.

By the formula, A = P (1 + RT/100) = 4000(1 + 5 x 5/100 ) = Rs. 5000

5.2 Compound Interest (C.I)

The compound interest is essentially interest over interest. The interest due is added to the

principal and that becomes the new principal for the interest to be levied. This method of interest

calculation is called compound interest. This can be for any period (yearly, half yearly or

quarterly) and will be called Period compounded like yearly compounded or quarterly compounded and so on.

First periods principal + first periods interest = second periods principal

Compound interest = principal (1 + )time - Principal

CI = P { 1 + }T P

Here Amount = principal (1 + )time

E.g. 2: Find the compound interest on Rs. 4500 for 3 years at 6 % per annum

Using the formula, A = P (1 + R/100)T = 4500(1 + 6/100)3 = 4500 (1.06)3 = 5360

Compound Interest = 5360 4500 = Rs 860

27

5.3 THE RULE OF 72 The rule of 72 is a quick way to show how long it will take to double your money. The equation

for the rule of 72 is:

Number of years for money to double = (72/Annual Interest Rate) interest rate

At 8% interest, it will take 72/8 = 9 years for your money to double.

Here are more examples:

At 6%, it will take 12 years (72/6 = 12).

At 12%, it will take 6 years (72/12 = 6).

The rule of 72 is a shortcut to estimate the magic of compound interest that makes your money

grow.

Remember that the rule of 72 is an approximation and its accuracy reduces as the interest rate becomes high.

Important notes

1. In case interest is paid half yearly, then the interest is divided by 2, and used as (R/2) in the formula and the time is multiplied by 2, and used as 2T in the formula, given by

A = P [1+ ]2T

E.g.3: Find the compound interest on Rs. 5000 for 3 years at 6 % per annum compounded half

yearly.

Using the formula, A = P [1 + ( R / 200 ) ]2T

= 5000(1 + 6/200)3x2

= 5000 (1.03)6 = 5971

Compound interest = 5971 5000 = Rs 971

2. In case, interest is paid quarterly, then the interest is divided by 4, and used as (R/4) in the

formula and the time is multiplied by 4, and used as 4T in the formula, given by

A = P [ 1 + ]4T payable quarterly (rate = R/4, time = 4T)

E.g.4: Find the compound interest on Rs. 5000 for 3 years at 6 % per annum compounded

quarterly.

Using the formula, A = P [1 + (R / 400 ) ]4T

= 5000(1 + 6/400)3x4

= 5000 (1.015)12 = 5978

Compound interest = 5978 5000 = Rs 978

3. In case the rates are different (R1, R2, R3.) for different years, the amount is given by P (1 + R1/100)(1 + R2/100)(1 + R3/100).

E.g.5: Find the compound interest on Rs. 5000 for 3 years at 6 % per annum for first year, 7% for

the second year and 8% for the third year.

Using the formula, P{1 + R1/100}{1 + R2/100}{1 + R3/100}

28

= 5000(1 + 6/100) (1 + 8/100) (1 + 9/100)

= 6125

Compound interest = 6125 5000 = Rs. 1125.

4. For population increase the formula to be used is P {1 + R/100 }T, and for decrease P { 1 -

R/100 }T. It can also be used for the depreciation factor.

E.g.6: The death rate of a town with population of 100000 is 5 %, considering there are no new

births, what is the population of town in next three years?

Using the formula, P {1 - R/100 }T

= 100000(1-5/100)3

= 100000(0.857) = 8573

6. The SI and CI earned during the first period remains the same.

E.g.7: The compound interest on a certain sum of money in 2 years is 210 and the simple interest

on the same amount is 200, what are the principle and the rate of interest?

Since SI and CI for first year is the same, and SI for each year is the same, so SI for the first year

= 200/2 = 100, CI for year I = 100, that means CI for the year II = 210 100 = 110. Here the excess of interest over year I = 10. Since the excess of interest in CI is interest over first years

interest, assuming I is the interest, I/100 x 100 = 10, so I = 10, and the principal is obviously

1000.(Try calculating it yourself)

E.g.8: A sum of money placed at Compound Interest doubles in every 5 years, then in how many

years it will become 16 times?

Now, it is given that the principle gets doubled in every 5 years. So, if we start from initial amount

P, then in first 5 years it will become 2P. In the next 5 years 2P will become 4P, next 5 years 4P

will become 8P and finally in the next 5 years 8P will become 16P.

So, it will take (5+5+5+5) = 20 years

5.4 Net Present Value (NPV)

Money received or paid today is not the same as money received or paid after a period. This is

because the money has an opportunity cost of interest in the same period. What it simply means is

that you can earn interest on money if you have it now, and if you get the money later, you lose

the opportunity to make interest on that. For example, if the going interest rate in the market is

10%, and someone has to pay me Rs. 1000, and he pays after an year, so he should pay, 1100 (100

has the interest), Here 1100 is called the future value and 1000 is called the present value.

Here the Future value (FV) = Present value (PV) {1 + Rate/100 }time, which is the basic formula

for amount in the case for compound interest, this is the formula to be used for calculating present

value. From here,

PV = FV / {1 + Rate/100 }time

This is the same formula as of the compound interest; herein we are calculating principal from the

amount, whichs it.

5.5 Equal annual installment to pay the debt amount

29

Let the borrowed (debt) amount = Rs. B, rate of interest per annum= R, amount of each

installment= Rs. A, and time = t yrs. Then,

a[ )+ 2 +.. t]= Borrowed amount B

E.g.9: What annual payment will discharge a debt of Rs. 50,440 due in 3 years at 5% per

annum compounded annually?

Let each annual installment= Rs. A. Then, by the formula,

A[ )+ 2 +.. t]=Borrowed amount B

A[ + 2 + 3]=50,440

A=Rs.18522

LEVEL 1

1. The SI on a sum of money is 25% of the principal, and the rate per annum is equal to the number

of years. Find the rate per cent.

(a) 4.5% (b) 6% (c) 5% (d) 8%

2. The rate of interest for first 3 years is 6% per annum, for the next 4 years, 7 per cent per annum

and for the period beyond 7 years, 7.5 percentages per annum. If a man lent out Rs 1200 for 11

years, find the total interest earned by him?

(a) 1002 (b) 912 (c) 864 (d) 948

3. A sum of money doubles itself in 12 years. Find the rate percentage per annum if interest is

calculated at simple interest.

(a) 12.5% (b) 8.33% (c) 10% (d) 7.51%

4. A certain sum of money amounts to Rs 704 in 2 years and Rs 800 in 5 years. Find the principal.

(a) Rs 580 (b) Rs 600 (c) Rs 660 (d) Rs 640

5. A sum of money was invested at SI at a certain rate for 3 years. Had it been invested at a 4%

higher rate, it would have fetched Rs 480 more. Find the principal.

(a) Rs 4000 (b) Rs 4400 (c) Rs 5000 (d) Rs 3500

6. A certain sum of money trebles itself in 8 years. In how many years it will be five times?

(a) 22 years (b) 16 years (c) 20 years (d) 24 years

7. If CI is charged on a certain sum for 2 years at 10% the amount becomes 605. Find the principal?

(a) Rs 550 (b) Rs 450 (c) Rs 480 (d) Rs 500

30

8. If the difference between the CI and SI on a certain sum of money is Rs 72 at 12 per cent per

annum for 2 years, then find the amount.

(a) Rs 6000 (b) Rs 5000 (c) Rs 5500 (d) Rs 6500

9. The population of Pune increases by 10% in the first year, it increases by 20% in the second year

and due to mass exodus, it decreases by 5% in the third year. What will be its population after 3

years, if today it is 10,000?

(a) 11,540 (b) 13,860 (c) 12,860 (d) 12,540

10. David borrows a sum of Rs 1200 at the beginning of a year. After 4 months, Rs 1800 more is

borrowed at a rate of interest double the previous one. At the end of the year, the sum of interest on

both the loans is Rs 216. What is the first rate of interest per annum?

(a) 9% (b) 6% (c) 8% (d) 12%

LEVEL 2

1) A sum of money invested at simple interest triples itself in 8 years at simple interest. Find in how

many years will it become 8 times itself at the same rate?

(a) 24 years (b) 28 years (c) 30 years (d) 21 years

2) A sum of money invested at simple interest triples itself in 8 years. How many times will it

become in 20 years time?

(a) 8 times (b) 7 times (c) 6 times (d) 9 times

3) If Rs. 1100 is obtained after lending out Rs. x at 5% per annum for 2 years and Rs. 1800 is

obtained after lending out Rs y at 10% per annum for 2 years, find x + y?

(a) Rs 2500 (b) Rs 3000 (c) Rs 2000 (d) Rs 2200

4) Peter borrows Rs 10000 at 20 % p. a. for 5 years at simple interest. From fourth year onwards, on

the entire amount due at the end of three years, the lender begins to charge 20% p. a. compounded

annually. What is the amount repaid by Peter after five years from the beginning?

(a) 23040 (b) 22500 (c) 21000 (d) 19900

5) Raj takes a loan at 100% p. a. interest. When he was repaying it after three years, he had to pay Rs

952000 more because the loan was compounded every moment, instead of annually. What was the

loan amount? [Take e=2.71 and (2.71)3=19.9]

(a) 78000 (b) 80000 (c) 80500 (d) 79500

6) A sum of money when kept at simple interest doubled in 8 years & 4 months. If rate of interest is

doubled and interest is calculated under compound interest in which year same sum will become

twice?

(a) 3rd Year (b) 4th Year (c) 5th Year (d) 6th Year

31

7) The population of a city is 200,000. If the annual birth rate and the annual death rate are 6% and

3% respectively, then calculate the population of the city after 2 years?

(a) 2, 12,090 (b) 2, 06,090 (c) 2, 12,000 (d) 2, 12,180

8) A part of Rs 38,800 is lent out at 6% per six months. The rest of the amount is lent out at 5% per

annum after one year. The ratio of interest after 3 years from the time when first amount was lent

out is 5 : 4. Find the second part that was lent out at 5%?

(a) 26,600 (b) 28,800 (c) 27,500 (d) 28,000

9) If the simple interest is 10.5 % annual and compound interest is 10% annual, find the difference

between the interests after 3 years on a sum of 1000?

(a) 15 (b) 12 (c) 16 (d) 11

10) A sum of 1000 after 3 years at compound interest becomes a certain amount that is equal to the

amount that is the result of 3 year depreciation from 1728. Find the difference between the rates of

CI and depreciation. (Given CI is 10% p.a.)?

(a) 3.33% (b) 0.66% (c) 3% (d) 2%

11) The Value of a machine depreciates 10% annually. If the present value of the machine is Rs 1, 00,

000/- then the total depreciation during 2 years hence will be?

(a) Rs 81, 000 (b) 21, 000 (c) Rs 19, 000 (d) Rs 72, 000

12) The present population of a village is 9, 261. If the annual birth rate is 81/2 % and the annual death

rate is 3.5%, then calculate the population 3 years ago.

(a) 10, 721 (b) 11, 363 (c) 11, 391 (d) 8, 000

13) A certain sum amounts to Rs 1, 452 in 2 years and to Rs 1, 597.20 in 3 years at compound

interest, then rate percent is?

(a) 10 (b) 11 (c) 13 (d) 9

14) The bacteria in a culture grows by 10% in first two hours, decreases by 10% in next on ehour and

again increases by 5% in next two hours. If the original count of the bacteria in the sample is 40,

000, find the bacteria count at the end of 5 hours?

(a) 48, 000 (b) 48, 025 (c) 48, 050 (d) 48, 075

15) The population of a town was 2, 50,000 three years ago. If it has increased by 3%, 4% and 6% in

the last three years, find the present population of the town?

(a) 2,83,868 (b) 2,81,686 (c) 2,82,868 (d) 2,80,168


1. What will Rs. 1500 amount to in three years if it is invested in 20% p.a. compound interest,

interest being compound annually? [ACCENTURE]

32

(A) 2592 (B) 2569 (C) 2540 (D) 2678

2. The difference between the compound interest and the simple interest earned at the end of 3rd year on a sum of money at a rate of 10% per annum is Rs. 77.5. What is the sum?

[ACCENTURE]

(A) Rs. 3500 (B) Rs. 3000 (C) Rs. 2000 (D) Rs. 2500

3. At a certain rate of simple interest a certain sum doubles itself in ten years. It will become four

times of itself in how many years? [PERSISTENT]

(A) 20 years (B) 15 years (C) 10 years (D) 5 years

4. Ajit invested Rs 35000 for 8 months and Manjit invested Rs 42000 for 10 months. On a profit of

Rs 31570 Ajit share is [VEDANTA]

(A) Rs.13548 (B) Rs.14234 (C) Rs.12628 (D) None of these

5. Anuj started a business by investing Rs.20, 000. Six months later, Pankaj joined him with a capital

of Rs.15,000. After another three months Puneet joined the team by investing Rs.50, 0000. Find

the ratio in which the profit at the end of two years should be divided by the three.

[ORACLE]

(A) 8:3:5 (B) 3:2:1 (C) 16:9:25 (D) 4:2:1

6. Mr. A lends 40% of a sum at 15% pa, 50% of the rest sum at 10% pa and the rest at 18% pa rate of

interest. What would be the rate of interest if the interest is calculated on the whole sum?

[Tech Mahindra]

(A) 13.4% pa (B) 14.33% pa (C) 14.4% pa (D) 13.33% pa

7. In simple interest what sum amounts of Rs.1120/- in 4 years and Rs.1200/- in 5 years?

[Tech Mahindra]

(A) 500 (B) 600 (C) 800 (D) 900

8. If a sum of money compound annually amounts of thrice itself in 3 years. In how many years will

it become 9 times itself? [Tech Mahindra]

(A) 6 (B) 8 (C) 10 (D) 12

9. In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3

of the time and C, the rest of the capital for the whole time. Out of a profit of Rs 4600, Bs share

will be? [L & T]

(A) Rs. 650 (B) Rs. 800 (C) Rs. 960 (D) Rs. 700

10. A sum of Rs. 370 is to be divided among A, B and C such that: = =

33

Then As share is [TCS]

(A) Rs. 240 (B) Rs. 120 (C) Rs. 100 (D) Rs. 90

ANSWER KEY LEVEL 1:

1 C 2 B 3 B 4 D 5 A 6 B 7 D 8 B 9 D 10 B

ANSWER KEY LEVEL 2:

1 B 2 C 3 A 4 A 5 B 6 B 7 D 8 B 9 C 10 D

11 C 12 D 13 A 14 B 15 A


1 A 2 D 3 A 4 C 5 C 6 C 7 D 8 B 9 A 10 D

CHAPTER 6

AVERAGES AND MIXTURES

6.1 Average:

Average is the mean value of a set of numbers of Values

Therefore Average = (x1+x2+x3.xn)/n

Ex: if the ages of four (4) students are 20,22,18 and 24 years respectively, find the average age.

Average = sum of ages =20+22+18+24 = 84 = 21

No. of students 4 4

6.2 Weighted Average :

Weighted average is the average of two or more groups whose individual averages are known

W.A = n1.a1 + n2.a2

n1+n2

6.3 Average Speed:

Average speed is the ratio of Total distance to the time taken

Average Speed = Total Distance

Total Time

6.4 Age and Average:

If the average age of n persons is decreased by a years then the total age decreases by ( na years and

vice versa)

34

Ex:The average weight of six men decreases by 3 kgs when a man whose weight is 60 kg is replaced by

another man. Find the weight of the man newly included.

Solution:

Decrease in total weight = 6 x 3 = 18 Kg so , the weight of the newly included man is 60-18 i.e is 42 kgs.

Note:- if a value which is less than the actual value is entered, then the average would reduce.

6.5 Rules of Allegation:

If two quantity are mixed in a ratio , then

Quantity of cheaper = cp of dearer Kean price Quantity of Dearer Mean price- Cp of Cheaper

Cp of cheaper(c) cp of dearer(d)

Mean Price(m)

(d-m) (m-c)

Ratio = x1 : x2

Hence , cheaper quantity : dearer quantity is (d-m): (m-c)

Container originally contains v units of liquid and K units of liquid is taken out of this operation is

repeated n times , then the final quantity of liquid in container is V [1- ]n units

Ex: for a container with 120 lts of milk, 40 lts is taken out and replaced with water , if this process is

repeated twice, find the quantity of milk in the container now?

Solution:

Quantity of milk in container

= 120 [1-40/120]

= 120[1-1/3]

35

=120 x 4/9

=53.33 ltrs

LEVEL 1

1. An airplane travels distance 2500 km, 1200 km and 500 km at speed 500 km/hr., 400 km/hr. and

250 km/hr. resp. The average speed of plane is

(A) 440 km/hr (B) 340 km/hr (C) 300 km/hr (D) 420 km/hr.

2. The average expenditure of a man for the first five months is Rs.120 and for the next seven months

it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :

(A) Rs.140 (B) Rs. 150 (C) Rs.160 (D) Rs. 170

3. The average age of 5 members is 21 years. If the age of the youngest member be 5 years, find the

average age of the family at the birth of the youngest member

(A) 20 years (B) 19 years (C)13 years (D) None of these

4. The average cost of 4 apples and 7 bananas is Rs.16, The average cost of 7 apples and 4 bananas is

Rs.24. The cost of 1 apple and 1 banana is Rs.

(A) 11 (B) 40 (C) 30 (D) 8

5. There are two groups A and B consisting of 30 and 70 students respectively, if the average weight

of Group A is 30 KGs and that of group B is 70 KGs find the average weight of all the students of

Group A and B

(A) 58 (B) 50 (C) 40 (D) 42

6. The average of marks obtained by 120 candidates was 35. If the average of marks of passed

candidates was 39 and that of failed candidates was 15, the number of candidates who passed the

examination is :

(A) 100 (B)110 (C) 120 (D) 150

7. The average temperature of the first three days is 27C and that of the next three days is 29C. If

the average of the whole week is 28.5C, the temperature of the last day of the week is :

(A) 10.5C (B) 21C (C) 31.5C (D) 42C

8. The average monthly expenditure of a family for the first four months is Rs. 2750, for the next

three months is Rs. 2940 and for the last five months is Rs. 3130.If the family saves Rs. 5330

during the whole year, find the average monthly income of the family during the year.

(A) Rs. 3800 (B) Rs. 3500 (C) Rs.3400 (D) Rs. 4200

9. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

(A) Rs. 7.98 (B) Rs. 8 (C) Rs. 8.50 (D) Rs. 9

36

10. The ratio of milk and water-milk mixture is 2:3.How much water should be added to 60 litres of

the mixture to make the ratio of milk and water as 1:3 ?

(A) 45 (B) 50 (C) 55 (D) 60

LEVEL 2

1. Nine litres are drawn from a cask full of wine and it is then filled with water, Nine litres of the

mixture are withdrawn and the cask is again filled with water. The ratio of quantity of wine now

remaining in the cask to that of water in it is 16:9.How much does the cask hold?

(A) 15 (B) 45 (C) 24 (D) none of these

2. A mixture contains brandy and water in the ratio 8: x. When 33 litres of the mixture and 3 litres of

water are mixed, the ratio of brandy and water becomes 2:1.The value of x is:


3. A sum of Rs. 39 was divided among 45 boys and girls. Each girl gets 50 paise, where as a boy

gets one rupee. Find the number of boys.


4. A container contains 1000 litres of Milk. From this container 100 litres of milk was taken out and

replaced by water .If this process was repeated three times , how much water is now contained by

the container?

(A) 729 lts (B) 700 lts (C) 656.1 lts (D) 271.0 lts

5. In what proportion must wheat at rs 11:00 per Kg be mixed with wheat at Rs. 16:00 per Kg so that

the mixture is worth Rs.13 per Kg?

(A) 2:3 (B) 3:2 (C) 11:16 (D) 16:11

6. If 3 Kg of metal , which is one third silver and rest aluminum is mixed with 7 Kg of another metal,

which is two-seventh silver and rest aluminum. What is the ratio of silver is to aluminum in the

mixture

(A) 3:7 (B) 7:3 (C) 1:7 (D) 2:7

7. A ten litres of water were added to ten litres of a 30% strong solution of sulphuric acid. Find the

strength of the resulting solution.

(A) 10% (B) 12% (C) 14.5% (D) 15%

8. Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be

mixed so that the mixture may be 15 times as heavy as water?

(A) 4:1 (B) 3:2 (C) 2:1 (D) 1:3

9. A trader has 100 kg of rice, a part of which he sells at 30% profit and the rest at 5% profit. He

gains 25% on the whole. What is the quantity sold at 30% gain?

(A) 80 kg (B) 40 kg (C) 75 kg (D) 35 kg

37

10. In two mixtures, spirit and water are related in the ratios of 3:5 and 7:4. 24 gallons of mixture I, 44

gallons of mixture II and 25 gallons of spirit are mixed together. What is the final ratio of spirit

and water?

(A) 2:1 (B) 1:5 (C) 5:2 (D) 1:6


1. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture, comprising of equal

quantities of all 3 samples is made. The proportion of milk and water in the mixture is

[ACCENTURE]

(A) 2:1 (B) 5:1 (C) 227:133 (D) 99:61

2. A certain quantity of petrol is found to be adulterated to the extent of 10%.What proportion of the

adulterated petrol should be replaced with pure petrol to take the purity level to 98% ?

[CAPGEMINI]

(A) 80% (B) 76% (C) 94% (D) None of these

3. There are 150 weights. Some are 1 kg weights and some are 2 kg weights .The sum of weights is

260. What is the number of 1 kg weights? [TCS]

(A) 50 (B) 30 (C) 65 (D) 40

4. Three friends A, B and C went for a weekend party to McDonalds restaurant and there they measure the weights in some order in 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 155 kg, then find

the average weight of all 7 rounds? [TCS]

(A) 29 kg (B) 30 kg (C) 28 kg (D) 31 kg

5. One quality of wheat costing Rs.9.30 per kg is mixed with another quality of wheat costing Rs. 10.80 per kg, then what will be the ratio in which they must be mixed so that the net cost is Rs. 10 per kg?

[VEDANTA]

(A) 5:7 (B) 8:7 (C) 13:19 (D) None of these

6. A 5 litre jug contains 4 litres of a salt water solution i.e it constitutes 15 percent salt. If 1.5 litres of

the solution spills out of the jug, and the jug is then filled to capacity with water, approximately

what percent of the resulting solution in the jug is salt? [HCL]

(A) 7.5% (B) 9.5% (C) 10.5% (D) 12%

7. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry

fruit can be obtained from 100 kg of fresh fruits? [WIPRO]

(A) 32 kg (B) 40 kg (C) 52 kg (D) 80 kg

38

8. A trader mixes rice of two qualities, the cost prices of which differ by Rs. 6, in a certain ratio to get the resultant cost price as Rs.12. If he mixes them in the reverse ratio and sells them at Rs.12, he gets a

profit of 20%. What is the cost (in Rs.) of the more expensive quality?

[COGNIZANT]

(A) 10 (B) 14 (C) 12 (D) 16

9. The average salary of 3 workers is Rs. 95 per week. If one earns Rs.115 and second earns Rs.65, how much is the salary of the 3rd worker? [CAPGEMINI]

(A) Rs.120 (B) Rs. 100 (C) Rs. 105 (D) None of these

10. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is

[COGNIZANT]

(A) 10 (B) 20 (C) 40 (D) 7

ANSWER KEY LEVEL 1:

1 D 2 B 3 A 4 D 5 A 6 A 7 C 8 C 9 A 10 D

ANSWER KEY LEVEL 2:

1 B 2 B 3 C 4 C 5 B 6 A 7 D 8 B 9 A 10 A


1 C 2 A 3 D 4 D 5 B 6 A 7 B 8 B 9 C 10 C

1

CHAPTER 7

TIME AND WORK

7.1 Work:

Quantity of work is directly proportional to the time taken i.e WT

Ex: If a man can reap 100 coins in 4 hours find the time taken by him to reap 5 coins?

WT

Therefore w/t is constant

100/4 = 5/9 ? = 20/100 (or) 1/5 hours

If A can do a piece of work in n days then in one day he can finish 1/n part of work in 1 day.

Ex: If a person can finish a work in 3 days then he can finish 1/3rd of work in 1 day.

If A can do a piece of work in N days and B in M , then both of them can finish the work in

N xM

M+N Days

Ex: If Rocia can do a piece of work in 4 days and Siya in 6 days , find the time taken by both of them to

finish the work

Solution:

Time taken to finish the work

= n xm / m + n days

= 6 x4 / 6 + 4 = 2.4 days

If A & B can do a work in n days , B and C in y days , C and A in z days then A,B,C working together can finish the work in 2x ( X x Y x Z) / X x Y + Y x Z + Z x X days

A can do it in y x d/ y-d days

B can do it in Z x d / Z- d days

C Can do it in X x d/ X- d days

D = (2 x X x Y x Z) / X x Y + Y x Z + Z x X

7.2 Efficiency:

2

Efficiency is the rate of doing work

1. Efficiency (E) is Inversely proportional to time E 1/t where E x T is constant

2. Efficiency E is directly proportional to Wages/ Works E W where E/W = constant

Ex: If A can finish a piece of work in 60 days find the time taken by B to finish the work given that B is

20% more efficient than A?

Solution :

Let the efficiency of A be 100%

Time taken by A is 60 days

Efficiency of B is 100+20= 120%

Efficiency 1/time Where EaTa = EbTb

Therefore 100 x 60= 120 x Tb

Where Tb= 50 days.

If a pipe can fill a tank in n hours and another pipe empties the same tank in m hours (n

3

a. Less than 6 days b. Exactly 6 days c. More than 6 days d. Exactly 10 days

3. Ajay can do a piece of work in 24 days; Sunil can do the same work in 8 days. If they work at it

on alternate days with Sunil beginning the work, then in how many the work will be completed?

a. 12 days b. 20 days c. 16 days d. none

4. A man can complete 3/8 of a work in 24 days . At this rate, how much more time is required to

complete the work?

a. 15 days b. 40 days c. 64 days d. 28 days

5. Mr. X can complete a job in 18 days , Mr.Y in 20 days and Mr. Z in 30 days , Mr. Y and Mr.Z

start the work and are forced to leave after 4 days . The time taken to complete the remaining

work by Mr.X is


6. Sharma and Shyam can do a piece of work in 24 days, Shyam and Shastri in 30 days , Shastri and

Sharma in 40 days. Who will take the least time to finish it alone?

a. Sharma b. Shyam c. Shastri d. None of these

7. If 3 women working for 6 hours a day earns Rs.650 in 10 days then how much will 18 women

working 9 hours a day earn in 10 days?

a. Rs. 6500 b. Rs. 5850 c. Rs. 925 d. none of these

8. Two pipes A and B can fill a tank in 1 hour 12 minutes and 1 hour 30 minutes, respectively. Pipe

C can empty the tank in 1 hour. Intially, Pipes A and B are opened and after 14 minutes C is also

opened. In how much time will the tank be full? (L-2)

a. 1 hour b. 80 min. c. 84 min. d. 1 hr 32 min.

9. Two pipes X and Y can fill a cistern in 15 min. and 40 min. respectively. Both pipes are opened

together but after 4 minutes, pipe X is turned off. What is the total time required to fill the

cistern?

a. 10 min 10 sec b. 25 min 20 sec c. 14 min 40 sec d. 20 min 10 sec

10. Some students can complete an assignment in 12 days. How many days will be taken by two

times the number of such students for 1/3rd of this assignment?


4

LEVEL 2

1) P is 30% more efficient than Q. P can complete a work in 23 days, If P and Q work together, how

much time will it take to complete the same work?

a. 9 b. 11 c. 13 d. 15

2) Peter, Qureshi and Ricky together earn Rs 1620 in 9 days. Peter and Ricky can earn Rs 600 in 5

days, Qureshi and Ricky in 7 days can earn Rs 910. How much amount does Ricky can earn per

day?

a. Rs 90 b. Rs 100 c. Rs 40 d. Rs 70

3) 3 men and 7 women can complete a work in 10 days. But 4 men and 6 women need 8 days to

complete the same work. In how many days will 10 women complete the same work?


4) Rohit and Mayank working together can finish a job in x days . If Rohit working alone takes 8

days more than x and Mayank working alone takes 18 days more than x , then what is the number

of days taken by Rohit and Mayank to complete the work together?

a. 10 days b. 8 days c. 12 days d. None of these

5) One Pipe can fill a tank 6 times as fast as another pipe. If together the two pipes can fill the tank

in 22 minutes , then the slower pipe will be able to fill the tank in:

a. 164 min b. 154 min c. 144 min d. 134 min

6) 25 men & 15 women do a piece of work in 12 days. They started the work , after 8 days women

leaves off the remaining work done by 25 men in 6 days. In how many days, 15 women can do

the same piece of work?


7) An empty tank be filled by an inlet Pipe A in 42 minutes. After 12 minutes an outlet Pipe B is

opened which can empty the tank in 30 minutes. After 6 minutes another inlet Pipe C opened into

the same tank , which can fill the tank in 35 minutes and the tank is filled. Find the time taken to

fill the tank?

a. 55 min b. 50.5 min c. 58.5 min d. 51.5 min

8) Two workers A and B working together completed a job in 5 days. If A worked twice as efficient

as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been

completed in 3 days. Find the time taken by A to complete the job alone.

5

a. 37/3 days b. 45/4 days c. 25/4 days d. 37/4 days

9) There is a leak in the bottom of the cistern, when the cistern had no leak it was filled in 2.5 hours,

it now takes half hour longer. If the cistern is full of water , how long will it take in leaking itself

empty, in case the water leaks out at double the rate after half the cistern becomes empty?

a. 15 hrs b. 11 hrs 15 min c. 11 hrs 25 min d. 7.5 hrs

10) Sahitya is thrice as good as Roshni and therefore is able to finish a job in 60 days less than

Roshni. What is the time taken to do twice the work, when they are working together?

a. 45 days b. 22.5 days c. 25 days d. 30 days.

11) Pipe A can fill a tank in 10 hours, Pipe B can fill the tank in 12 hours, but if the pipe A is opened for 5 hours and then pipe B is opened for 6 hours, how much time in hours it is required to fill the

rest of the tank by pipe A and pipe B together?

a. 20 b. 10 c. 15 d. 0

12) A pipe can fill a tank in x hours and another can empty it in y hours. If the tank is 1/ 3rd full then

the number of hours in which they will together fill it in is

(A) 3xy/2(y-x) (b) 3xy/y-x (c) xy/3(y-x) (d) 2xy/3(y-x)

13) A finishes 6/ 7th of the work in 2z hours, B works twice as fast and finishes the remaining work.

For how long did B work?

(A) (2/3)z (b) (6/7)z (c) (6/49)z (d) (3/18)z

14) Ajit can do as much work in 2 days as Baljit can do in 3 days and Baljit can do as much in 4 days

as Diljit in 5 days. A piece of work takes 20 days if all work together. How long would Baljit take

to do all the work by himself?

(A) 82 days (b) 44 days (c) 66 days (d) 50 days

15) Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously

and it is found that due to leakage in the bottom of the cistern, it takes 32 minutes extra for the

cistern to be filled up. When the cistern is full, in what time will the leak empty it?

(A) 114 h (b) 112 h (c) 100 h (d) 80 h

---------------------------------------------------------------------------------------------------------------------


6

1. Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can

do the same job in 9 hours. If Tina works independently at the job for 8 hours and then Ann

works independently, how many hours will it take Ann to complete the remainder of the jobs?

[HCL]

(A) 2/3 (B) 3/4 (C) 1 (D) 3

2. A and B can together complete a piece of work in 12 days. A alone can complete in 20 days. If B

does the work only for half a day daily, then in how many days A and B together will finish the

job? [L&T]

(A) 10 (B) 11 (C) 20 (D) 15

3. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in

4 days. 6 men start working on the job and after working for two days, all of them stop working.

How many women should be put on the job to complete the remaining work, if it is to be

completed in 3 days? [COGNIZANT]

(A) 22 (B) 15 (C) 24 (D) Data inadequate

4. Anil and Suman can complete a work in 10 and 15 days, respectively. Anil starts the work, and

after 2 days, Suman joins him. But Suman leaves him after 2 days. How many more days will

Anil now have to work to complete it? [ACCENTURE]

(A) 2.75 days (B) 3 days (C) 4.66 days (D) 5 days

5. A can have a piece of work done in 8 days, B can work three times faster than A, C can work five times faster than A. How many days will they take to do the work together?

[TECH MAHINDRA]

(A) 3 days (B) 8/9 days (C) 4 days (D) Can't say

6. There are two pipes in a tank. Pipe A is for filling the tank and Pipe B is for emptying the tank. If A can fill the tank in 10 hours and B can empty the tank in 15 hours then find out how many

hours it will take to completely fill a half empty tank? [ACCENTURE]

(A) 30 hours (B) 15 hours (C) 20 hours (D) 33.33 hours

7. A can do a work in 90 days, B in 40 days and C in 12 days. They worked for a day each in turn, i.e. A worked alone for the first day, B for the second day and C for the third day, then again A

and so on. After finishing the work, they got Rs.240. Wages were divided in proportion to the

work done by them. As share is: [TCS]

(A) Rs. 24 (B) Rs. 28 (C) Rs. 60 (D) Rs. 88

7

8. It is often said, Rome was not built in a day. But if there are 2000 walls in Rome and each wall has 3000 bricks. It takes 2 seconds for one worker to fix a brick. How much time would have

been taken to build Rome if there were 100 such workers? [ZENSAR]

(A) less than a day (B) 1-2 days (C) 2-3 days (D) 4-5 days

9. Worker W produces n units in 5 hours. Workers V and W, work independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n unit [HCL]

(A) 1 hr 26 min (B) 1 hr 53 min (C) 2 hr 30 min (D) 3 hr 20 min

10. 20 labourers can do a work in 20 days, if everybody works for 6 hours daily. Then 25 labourers can do the same work in 12 days by working daily for: [INFOSYS]

(A) 8 hours (B) 6 hours (C) 4 hours (D) 10 hours

ANSWER KEY LEVEL 1:

1 D 2 B 3 A 4 B 5 A 6 B 7 BA 8 D 9 B 10 C

ANSWER KEY LEVEL 2:

1 C 2 D 3 B 4 C 5 B 6 A 7 C 8 C 9 C 10 B

11 D 12 D 13 D 14 C 15 B


1 D 2 D 3 B 4 C 5 B 6 B 7 A 8 B 9 D 10 A

CHAPTER 8

TIME, SPEED AND DISTANCE

8.1 Speed:

8

Speed = Distance/ Time or Distance = Speed x Time

1. Speed is directly proportional to distance

2. Distance is directly proportional to time

3. Speed and time are inversely proportional

8.2 Conversion Factors:

1 Km/Hr = 5/18 m/s

1 M/S = 18/5 Km/Hr

Ex: A bowler has a run up of 150 m. if the speed of the bowler is 54 kmph, how much time would he take

to complete the run up?

Solution:

54 km/Hr = 54 x 5/18 m/s = 15 m/s

Time = distance /speed =150/15 = 10 sec.

In travelling equal distance with speeds of X and Y , the average speed is given by

(2XY)/X+Y

Ex: Find the average speed of a car that covers 1st 50% of distance at 40 Km/Hr and the 2nd 50% of the

distance at 60 Km/ Hr.

Solution:

Average speed = 2 x X x Y / X+Y

= 2 x 60 x 40/ 60 +40

=4800/100=48 km/hr

8.3 Relative Speed :

The speed of a body with the respect to another moving body is defined as relative speed.

If two bodies are moving in same direction , the relative speed is given by the difference of speeds.

X

y

9

Relative speed = (X-Y)

If two bodies are moving in the opposite direction, then the relative speed is given by the sum of the

speeds.

X

Y

Relative speed = (X+Y)

Ex: If two trains of length 200m and 250m are having speed 18 km/hr and 36 km/ hr , find the time taken

to cross each other

1. If they move in the same direction

2. If they move in opposite direction

Solution:

Speed of first train = 18 x 5/18= 5m/s

Speed of second train = 36 x 5/18= 10 m/s

Distance they have to cross to cross each other is the sum of lengths of train = 200 + 250 =450m

If they move in same direction, relative speed = 10-5 = 5 m/s

Time taken = distance /Speed= 450/5 = 90 sec

If they move in oppo

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