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Manual for Corporate Recruitment

Preface

The book is mainly targeted to provide the graduates, who are looking for their placements in companies from various sectors, with the most comprehensive book that can help them prepare to crack the aptitude tests.

The approach of the book is different from other aptitude and reasoning books available in the market in a way that it concentrates more on the logic behind the problems rather on the formulae to solve them.

There had been a necessity for a book that can serve the needs of the graduates seeking their placements and this book can provide the best solution.

It is designed in such a way that all the concepts required to be prepared in by the students to crack the aptitude test conducted by the companies are discussed in detail with required synopsis and examples.

The following are the topics that will be covered in this book: I. Selection Processes of various MNC’s:

This makes the students aware of the recruitment processes of various MNC‟s with detailed description of all the rounds of selection and the qualities that the candidate has to develop to pass it.

II. Quantitative Aptitude:

This section deals with all the topics related with arithmetic problems, the logics behind each concept and applying the logics for solving the problems.

All the exercises and the tests are provided with solutions to help the readers check their approaches to the problems.

III. Logical Aptitude:

This section deals with problems related with Logical and Analytical reasoning, explaining all the concepts with vivid logics behind them. All the problems and the tests are provided with solutions to help the reader to understand better.

IV. Verbal Aptitude:

This section deals with testing the reader on his knowledge of English language and this is one of the sections in the aptitude section of the test conducted by the companies. It will help the readers to improve their vocabulary, comprehension, functional grammar and sentence structures. Outstanding Features:

1. Every concept is explained more clearly with logic behind the concept, without the usage of numerous formulae. This provides the readers with a better level of understanding over the topics.

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2. Every logic is strengthened by solved examples, exercises, tests and solutions to ensure that the reader gets all the required inputs at the required level of complexity.

3. The CD contains Diagnostic Tests, Vocabulary Building List and Practice Papers with real-time difficulty to provide the user with extra benefits.

In all, there is a guarantee that this book will be a very helpful and effective tool for the job-seekers by providing them with all the inputs and guiding them towards their placement in the companies.

Recruitment Patterns of various MNC’s

Various MNC‟s have different patterns for recruitment but the skeletal structure of the patterns is commonly aid to be as follows:

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Round I: Written test on aptitude

Round II: Written test on technical knowledge Round III: Group Discussion

Round IV: Technical Interview Round V: HR Interview

So unless you prove yourself in aptitude test you will never get a chance to prove any other expertise you possess in other aspects.

This is the reason why aptitude is considered the most important factor by the aspirants of various MNC recruitments.

Importance of aptitude in recruitment process

Aptitude test is the first round of recruitment process for any company in any sector like Banking, Software, Insurance, Pharmaceutics etc. All the graduates with 60% or above are eligible for the recruitment process and everyone is tested on the same

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grounds of aptitude. This gives us the clear idea that the companies are giving aptitude more importance than the academic percentages.

What is aptitude?

Aptitude literally means a natural talent. It is something that comes with us by our birth. But it is to be explored and developed within by us and that can be achieved by understanding and practicing the concepts of aptitude.

The candidates with good aptitude skills are considered better than others because they are fast at their mind and good at problem solving skills. Thus aptitude has become the most important soft skill these days.

Why aptitude?

Even if the candidate is good at academics and communication skills, he will not get a chance to prove them unless he passes through the initial round of aptitude

testing. So we can conclude that without appropriate levels of aptitude an aspirant can never achieve success in the recruitment process of any corporate sector

company.

This book helps all the aspirants in clearly understanding the concepts of aptitude that are required for the recruitment processes of various companies. For further practice on these concepts covered in the book you can refer to the books on aptitude by Pearson Education like Test of reasoning and general intelligence by Showick Thorpe and Quantitative Techniques by Khattar.

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QUANTITATIVE

APTITUDE

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Percentages

Understanding Percentages:

The word percent can be understood as follows:

Per cent => for every 100.

So, when percentage is calculated for any value, it means that that you calculate the value for every 100 of the reference value.

Why Percentage?

Percentage is a concept evolved so that there can be a uniform platform for

comparison of various things. (Since each value is taken to a common platform of 100.)

Eg: To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another.

Before going deeper into the concept of percentage, let u have a look at some basics and tips for faster calculations:

Calculation of Percentage:

Percentage = (Value / Total value) X 100 Eg: 50 is what % of 200?

Soln: Percentage = (50/200) X 100 = 25%. Calculation of Value:

Value = (Percentage/100) X total value Eg: What is 20% of 200?

Soln: Value = (20/100) X 200

Note: Percentage is denoted by “%”, which means “/100”. Eg: What is the decimal notation for 35%?

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For faster calculations we can convert the percentages or decimal equivalents into their respective fraction notations.

Percentages – Fractions Conversions:

The following is a table showing the conversions of percentages and decimals into fractions:

Percentage Decimal Fraction

10% 0.1 1/10 12.5% 0.125 1/8 16.66% 0.1666 1/6 20% 0.2 1/5 25% 0.25 1/4 30% 0.3 3/10 33.33% 0.3333 1/3 40% 0.4 2/5 50% 0.5 1/2 60% 0.6 3/5 62.5% 0.625 5/8 66.66% 0.6666 2/3 70% 0.7 7/10 75% 0.75 3/4 80% 0.8 4/5 83.33% 0.8333 5/6 90% 0.9 9/10 100% 1.0 1

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Similarly we can go for converting decimals more than 1 from the knowledge of the above cited conversions as follows:

We know that 12.5% = 0.125 = 1/8

Then, 1.125 = [8(1)+1]/8 = 9/8 (i.e., the denominator will add to numerator once, denominator remaining the same.

Also, 2.125 = [8(2)+1]/8 = 17/8 (here the denominator is added to numerator twice) 3.125 = [8(3)+1]/8 = 25/8 and so on.

Thus we can derive the fractions for decimals more than 1 by using those les than 1.

We will see how use of fractions will reduce the time for calculations: Eg: What is 62.5% of 320?

Soln: Value = (5/8) X 320 (since 62.5% = 5/8) = 200.

Percentage Change:

A change can be of two types – an increase or a decrease. When a value is changed from initial value to a final value,

% change = (Difference between initial and final value/initial value) X 100 Eg: If 20 changes to 40, what is the % increase?

Soln: % increase = (40-20)/20 X 100 = 100%. Note:

1. If a value is doubled the percentage increase is 100.

2. If a value is tripled, the percentage change is 200 and so on. Percentage Difference:

% Difference = (Difference between values/value compared with) X 100. Eg: By what percent is 40 more than 30?

Soln: % difference = (40-30)/30 X 100 = 33.33%

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Eg: By what % is 60 more than 30?

Soln: % difference = (60-30)/30 X 100 = 100%. (Here is 60 is compared with 30.)

Hint: To calculate percentage difference the value that occurs after the word “than” in the question can directly be used as the denominator in the formula.

Important Points to Note:

1. When any value increases by

a. 10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1) b. 20%, it becomes 1.2 times of itself.

c. 36%, it becomes 1.36 times of itself. d. 4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases. 2. When any value decreases by

a. 10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9) b. 20%, it becomes 0.8 times of itself

c. 36%, it becomes 0.64 times of itself d. 4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases. Note:

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on.

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Soln: 30% decrease => 0.7 x.

Eg: A value after an increase of 20% became 600. What is the value? Soln: 1.2x = 600 (since 20% increase)

 x = 500.

Eg: If 600 is decrease by 20%, what is the new value? Soln: new value = 0.8 X 600 = 480. (Since 20% decrease)

Thus depending on the decimal we can decide the % change and vice versa.

Eg: When a value is increased by 20%, by what percent should it be reduced to get the actual value?

Soln: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula) % decrease = (1.2 – 1)/1.2 X 100 = 16.66%.

3. When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes.

Eg: The population of a town increased by 10%, 20% and then decreased by 30%. The new population is what % of the original?

Soln: The overall effect = 1.1 X 1.2 X 0.7 (Since 10%, 20% increase and 30% decrease)

= 0.924 = 92.4%.

Eg: Two successive discounts of 10% and 20% are equal to a single discount of ___ Soln: Discount is same as decrease of price.

So, decrease = 0.9 X 0.8 = 0.72 => 28% decrease (Since only 72% is remaining).

Exercise:

1. If 20% of 40% of a = 25% of a% of b, then what is b?

a. 8/5 b. 16/25 c. 8/25 d. None

2. By what % is 200 more than 50?

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3. A value changes from 30 to 80. What is the percentage change?

a. 125 b. 166.66 c. 156 d. None

4. The population of a city is increased by 30% and thus became 78000. What is the original population?

a. 76000 b. 64200 c. 60000 d. None

5. In a theatre, the number of seats is increased by 20% and the price per ticket is increased by 10% but the public response decreased by 30%. What is the net effect on the economy of the theatre?

a.10% rise b. 7% fall c. 7% rise d. None

6. A saves 20% of his income. His income is increased by 20% and so he increased his expenditure by 30%. What is the percentage change in his savings?

a. 20% fall b. 4% fall c. 20% rise d. 4% rise

7. The price of petrol is increased by 25%. By what percent the consumption be reduced to make the expenditure remain the same?

a. 25% b. 33.33% c. 20% d. None

8. The side of a square is increased by 20%. The percentage change in its area is ___

a. 20% b. 44% c. 36% d. None

9. If the length of a rectangle is increased by 33.33%, by what percentage should the breadth be reduced to make the area same?

a. 20% b. 33.33% c. 25% d. None

10. In an election between two candidates, A and B, A secured 56% of the votes and won by 48000 votes. Find the total number of votes polled if 20% of the votes were declared invalid.

a. 500000 b. 400000 c. 600000 d. None

11. A reduction of 10% in price of sugar enables a housewife to buy 5 kg more for Rs. 300/-. Find the reduced price per kg of sugar.

a. 5/- b. 4.5/- c. 6/- d. None

12. From a 20lt solution of alt and water with 20% salt, 2lt of water is evaporated. Find the new % concentration of salt.

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13. In a list of weights of candidates appearing for police selections, the weight of A is marked as 58 kg instead of 46.4 kg. Find the percentage of correction required.

a. 30 b. 20 c. 24 d. None

14. A person spends 20% of his income on rent, 20% of the rest on food, 10% of the remaining on clothes and 10% on groceries. If he is left with Rs. 9520/- find his income.

a. 10000/- b. 15000/- c. 20000/- d. None

15. A shopkeeper offers three successive discounts of 10%, 20% and 30% to a

customer. If the actual price of the item is Rs. 10000, find the price the custome has to pay to the shopkeeper.

a. 5040/- b. 4000/- c. 6000/- d. None

16. If 10lt solution of water and alcohol containing 10% alcohol is to be made 20% alcohol solution, find the volume of alcohol to be added.

a. 1 lt b. 1.25 lt c. 1.5 lt d. 2 lt

17. A is twice B and B is 200% more than C. By what percent is A more than C?

a. 400 b. 600 c. 500 d. 200

18. In an examination, a student secures 40% and fails by 10 marks. If he scored 50%, he would pass by 15 marks. Find the minimum marks required to pass the exam.

a. 250 b. 100 c. 110 d. 125

19. If A is 20% taller than B, by what percent is B shorter than A?

a. 20% b. 25% c. 16.66% d. None

20. The population of a town increases at a rate of 10% for every year. If the present population is 12100, find the population two years ago.

a. 11000 b. 9800 c. 10000 d. 10120

21. A solution of salt and water contains 15% salt. If 30 lt water is evaporated from the solution the concentration becomes 20% salt. Find the original volume of the liquid before water evaporated.

a. 100 lt b. 120 lt c. 200 lt d. None

22. If 240 lt of oil is poured into a tank, it is still 20% empty. How much more oil is to be poured to fill the tank?

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a. 300 lt b. 60 lt c. 120 lt d. None

23. A and B were hired for the same salary. A got two 40% hikes whereas B got a 90% hike. What is the percentage difference in the hikes thay got?

a. 16% b. 6% c. 10% d. 8%

24. The population of a town doubled every 5 years from 1960 to 1975. What is the percentage increase in population in this period?

a. 800 b. 400 c. 700 d. 600

25. In a test of 80 questions, Jyothsna answered 75% of the first 60 questions correctly. What % of the remaining questions she has to answer correctly so that she can secure an overall percentage of 80 in the test?

a. 80% b. 90% c. 85% D. 95% Solutions: 1. 1/5 X 2/5 X a = ¼ X a X b => b = 8/25 2. % difference = (200-50)/50 X 100 = 300 % 3. % increase = (80-30)/30 X 100 = 166.66 % 4. 1.3 x = 78000 => x = 60000. 5. Net effect = 1.2 X 1.1 X 0.7 = 0.924 => 7.6% decrease. 6. Let I be the income.

Expenditure = 0.8I Savings = 0.2I => 20% New income = 1.2I (since 20% rise)

New expenditure = (0.8I) X 1.3 (Since 30% rise) = 1.04I

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(So income decreased form 20% to 16%) % decrease = (20-16)/20 X 100 = 20%. 7. It is equivalent to 1.25 decreased to 1.

% decrease = (1.25-1)/1.25 X 100 = 20%

8. % change in area = 1.2 X 1.2 (since area = side X side) = 1.44 => 44%.

9. It is equivalent to 1.25 decreased to 1. So 20% decrease. 10. Valid Votes:

A got 56% => B got 44% Difference = 12% = 48000

So, 100% = 400000. These are valid votes. But valid votes are only 80% of total votes.

So, 80% of total votes = 400000 => total votes = 500000 11. Total money = Rs. 300.

Saving of the lady = 10% of 300 = 30/-

With 30/- she bought 5 kg sugar => each kg costs Rs. 6/- 12. In 20lt, salt = 20% => 4 lt.

New volume = 18 lt (2 lt evaporated) So, new % = 4/18 X 100 = 22.22%

13. % correction = (58-46.4)/58 X 100 = 20%

14. Three successive decreases of 20%, 20% and 10% => 0.8 X 0.8 X 0.9 = 0.576

Again 10% decrease => 0.576 – 0.1 = 0.476. So, 0.476 x = 9520 => x = 20000.

15. Total discount = 0.9 X 0.8 X 0.7 = 0.504 of actual price. So, price = 0.504 X 10000 = 5040.

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16. In 10 lt, alcohol is 10% = 1 lt. Let x lt alcohol is added.

So, (1+x)/(10+x) = 20% = 1/5 => x = 1.25 lt. 17. A = 2B and B = 3C (ince 200% more)

 A = 6C => 500 % more.

18. 50% of max marks – 40% of max marks = 25  max marks = 250

Pass marks = 40% of max + 10 => 100 + 10 = 110. 19. A = 1.2 B => B = A/1.2 => 0.8333A => 16.66%.

(OR) Decrease from 1.2 to 1 => 16.66%. 20. 1.1 X 1.1 X x = 12100 => x = 10000.

21. Salt = 15% of x = 0.15x (x = volume of solution) Now, 0.15x/(x-30) = 20% = 1/5 (since 30 lt evaporated)  x = 120 lt

22. 20% empty => 80 % full = 240 lt => 20% = 60 lt 23. A => 1.4 X 1.4 = 1.96

B => 1.9 => 6% difference.

24. From 1960 to 1975, in 15 years population doubled every 5 yrs => three times So, 2 X 2 X 2 = 8 times => 700% more.

25. [(75% X 60) + (x% X 20)] / 80 = 80% => x = 95. (since required is 80%)

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Profit and Loss What is Profit?

When a person does a business transaction and gets more than what he had invested, then he is said to have profit. The profit he gets will be equal to the additional money he gets other than his investment.

So profit can be understood as the extra money one gets other than what he had invested.

Eg: A person bought an article for Rs. 100 and sold it for Rs. 120. Then he got Rs. 20 extra and so his profit is Rs. 20.

What is Loss?

When a person gets an amount less than what he had invested, then he is said to have a loss. The loss will be equal to the deficit he got than the investment. Eg: A person bought an article at Rs. 100 and sold it for Rs. 90. Then he got a deficit of Rs. 10 and so his loss is Rs. 10.

Cost Price (CP):

The money that the trader puts in his business is called Cost Price. The price at which the articles are bought is called Cost Price.

In other words, Cost Price is nothing but the investment in the business. Selling Price (SP):

The price at which the articles are sold is called the Selling Price. The money that the trader gets from the business is called Selling Price.

In other words, Selling Price is nothing but the returns from a business. Marked/Market/List Price (MP):

The price that a trader marks or lists his articles to is called the Marked Price. This is the only price known to the customer.

Discount:

The waiver of cost from the Marked Price that the trader allows a customer is called Discount.

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Note:

1. Profit or loss percentage is to be applied always to the Cost Price only. 2. Discount percentage is to be applied always to the Marked Price only. Relationship Among CP, SP and MP:

A trader adds his profit to the investment and sells it at that increased price. Also he allows a discount on Marked Price and sells at the discounted price. So, we can say that,

o SP = CP + Profit. (CP applied with profit is SP)

o SP = MP – Discount. (MP applied with discount is SP) Understanding Profit and Loss:

So, by now we came to know that if CP is increased and sold it would result in profit and vice versa.

Also whatever increase is applied to CP, that increase itself is the profit.

For Rs. 10 profit, CP is to be increased by RS. 10 and the increased price becomes SP.

For 10% profit, CP is to be increased by 10% and it is the SP.

(From previous chapter we know that any value increased by 10% becomes 1.1 times.)

So, for 10% profit, CP increased by 10% => 1.1CP = SP. o SP = 1.1CP => SP/CP = 1.1 => 10% profit o SP = 1.07CP => SP/CP = 1.07 => 7% profit

o SP = 1.545CP => SP/CP = 1.545 => 54.5% profit and so on. Similarly,

o SP = 0.9CP => SP/CP = 0.9 => 10% loss (Since 10% decrease) o SP = 0.76CP => SP/CP = 0.76 => 24% loss and so on.

So, to calculate profit % or loss %, it is enough for us to find the ratio of SP to CP.

Note:

1. If SP/CP > 1, it indicates profit. 2. If SP/CP < 1, it indicates loss. Multiple Profits or losses:

A trader may sometimes have multiple profits or losses simultaneously. This is equivalent to having multiple changes and so all individual changes are to be multiplied to get the overall effect.

Examples:

1. A trader uses a 800gm weight instead of 1 kg. Find his profit %. Soln: (He is buying 800 gm but selling 1000 gm.

So, CP is for 800 gm and SP is for 1000 gm.) SP/CP = 1000/800 = 1.25 => 25% profit.

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2. A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his profit/loss %.

Soln: 1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8 20% increase in price => profit (increase) => 1.2

So, net effect = (0.8) X (1.2) = 0.96 => 4% loss.

3. A milk vendor mixes water to milk such that he gains 25%. Find the percentage of water in the mixture.

Soln: To gain 25%, the volume has to be increased by 25%.

So, for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt % of water = 0.25 / 1.25 X 100 = 20%.

4. A trader bought an item for Rs. 200. If he wants a profit of 22%, at what price must he sell it?

Soln: CP=200, Profit = 22%.

So, SP = 1.22CP = 1.22 X 200 = 244/-.

5. A person buys an item at Rs. 120 and sells to another at a profit of 25%. If the second person sells the item to another at Rs. 180, what is the profit % of the second person?

Soln: SP of 1st_{person = CP of 2}nd_{person = 1.25 X 120 = 150.}

SP of 2nd_{person = 180.}

Profit % = SP/CP = 180/150 = 1.2 => 20%.

6. A milk vendor mixes water to 20 lt of milk such that the ratio of milk and water is 4:3. He sold the mixture at Rs. 12 per liter but bought the milk at Rs. 10 per liter. Find the profit % of the vendor.

Soln: milk : water = 4:3 => he bought 4 parts (milk) but sold 7 parts (mixture) CP = 10 and SP = 12.

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So, profit % = (SP/CP) X (SP/CP) = (7/4) X (12/10) = 2.1 => 110% gain.

7. A trader buys some apples at a price of 10 apples for Rs. 8 and sold them at a price of 8 apples for Rs. 10. Find his profit or loss %.

Soln: He bought 10 apples for Rs. 8 and sold 8 apples for Rs. 10 => clearly got profit

 SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625 => 56.25 % gain.

8. A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the CP should be marked on the items?

Soln: CP applied with profit = MP applied with discount = SP

 1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP. 9. By selling an item at a price a trader gains 40%. What is the profit / loss % if

the item is sold at half the price?

Soln: SP =1.4CP => (SP/2) = 0.7CP => 30% loss.

10. A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual CP of the article.

Soln: 25% gain => SP = 1.25CP…..1.

Now, CP is 10% less => 0.9CP and SP is Rs. 2 less => (SP-2).

Still, profit is 25% => (SP-2)=1.25(0.9CP) , where SP = 1.25CP (From 1)  CP = Rs. 16.

11. A trader gets a discount of 20% from the dealer and marks it at 20% more price then the actual MP to the customer. Find his overall gain %.

Soln: Let MP be the price on the item.

Then, CP=0.8MP (20% discount) and SP = 1.2MP. So, gain => SP/CP = 1.2/0.8 = 1.5 => 50%.

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12. A trader allows a discount of 20% to the customer after marking the item up by 25%. Find his gain/loss% if he is given a commission of 20% of the MP by the dealer.

Soln: Trader‟s SP = 0.8 X (1.25MP) = MP (since 20% discount on 25% raised price)

Trader‟s CP = 0.8 MP (20% commission) So, gain = SP/CP = MP/0.8MP = 1.25 => 25%.

Exercise:

1. The profit obtained by selling an article for Rs.56 is the same as the loss obtained by selling it for Rs.42. What is the cost price of the article?

1) Rs.40 2) Rs.50 3) Rs.49 4) None of these

2. A dealer professes to sell his goods at cost price and uses an 880gm weight instead of a kg. What is his percentage of gain?

1) 13.13% 2) 13.33% 3) 13.36% 4) 13.63%

3. P sold an article for Rs.1,080 thereby losing 10% Q sold another article for Rs.1,800 at a loss of 10%. Who incurred a greater loss?

1) P 2) Q 3) Cannot say 4) Both have equal

4. Swapna 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 her?

1) 100% 2) 150% 3) 125% 4) None of these

5. By selling some cloth at the cost price a merchant still gained 191_/₂₁_{%. How}

much less cloth does he measure for a meter?

1) 15cm 2) 16cm 3) 20cm 4) None of these

6. 30% loss on cost price in what percent loss on selling price?

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7. Arun purchased a house for Rs.75,000 and a site for Rs.15,000 respectively, if he sold the house for Rs.83,000 and the site for Rs.10,000, then find the resultant percentage of gain?

1) 3% 2) 31_/₃_% _{3) 30%} _{4) 33}1_/₃_%

8. The manufacturing cost of a watch is Rs.180 and the transportation lost is Rs.500 for 100 watches. What will be the selling price if it is sold at 20% gains

1) Rs.222 2) Rs.216 3) Rs.221 4) Rs.220

9. A person, by selling an article at three-fourths of the list price incurs a loss of 20%. Find the profit percentage if he sells at the list price?

1) 25% 2) 6.66% 3) 111_/₉_% _{4) None of these}

10. A sells an article to B at a gain of 20%. B sells is to C at a gain of 25% and C in turn sells is to D at a loss of 331_/₃_{%. If D paid Rs.1,000 for it, then what is the}

cost price of A.

1) Rs.1,000 2) Rs.2,000 3) Rs.3,000 4) Rs.4,000

11. Ajay had purchased a second hand scooter for 18,000 and spent Rs.1,800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 111_/₉_{%, if 9}1_/₁₁_{% is to be deducted at the end of every year on account of}

deprecation?

1) Rs.18,000 2) Rs.19,800 3) Rs.20,000 4) Rs.22,500

12. After getting three equal successive discount percentages over a marked price of Rs.1,000 a customer has to pay 729 for an article. What is the rate of each of the successive discounts?

1) 10% 2) 20% 3) 30% 4) 40%

13. One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader?

1) 20%gain 2) 162_/₃_{% loss} _{3) 14}2_/₇_%gain _{4) 10%loss}

14. Due to a slump in the market, A, while selling 12 apples to B, allows him to count them as 9. But due to an overnight demand A is forced to buy them back at the same rate as he sold and allows B to count 9 apples as 12. What is overall gain percentage of B

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15. A trader offers to give two articles free for every 10 articles I purchase. I get a total of 10 articles free for my purchase and I sell them all at a rate such that I get back my investment from the sale of just 10 of the articles. What is my overall percentage of profit

1) 100% 2) 150% 3) 500% 4) 250%

16. A mechanic purchases a cooler for Rs.32,000 and incurs Rs.13,000 on

installation and repairs. After one year he sold it for Rs.40,000. What is the profit or loss percentage, if the deprecation rate of the machine is 20% p.a?

1) 81_/₃_% _{2) 12}1_/₁₂_% _{3) 16}1_/₄_% _{4) 11}1_/₉_%

17. Ramya bought a certain number of apples at 6 apples for Rs.10 and sold them at 4 apples for Rs.10. Find the number of apples she bought if total gain is Rs.60

1) 30 2) 31 3) 62 4) None of these

18. 5kg of ghee was bought by Venu for Rs.300. One kg becomes spoilt. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg does he sell the ghee?

1) Rs.46.25 2) Rs.45.70 3) Rs.46.60 4) Rs.67.50

19. A trader professes to lose 10% in selling 2kgs of rice. He uses 2 weighing stones, each of which is marked 1kg but weighs less. If the percentage of profit is 26_/₇_%

and one of the two stones weighs only 800 gm, how much does the second stone weigh

1) 800gm 2) 850gm 3) 900gm 4) 950gm

20. A girl sold her pen for Rs.39 and got a percentage of profit numerically equal to the cost price. The cost price of that pen is..

21. A person loses 10% on one investment but gains 20% on another. If the ratio of the investments is 3:4, what is the percentage of gain or loss on the two

investments taken together?

1) 61_/₈_% _{2) 7}1_/₇_% _{3) 11}1_/₉_% _{4) None of these}

22. A trader professes to sell all articles at a loss of 25%, but sells three-fifth of them at again of 25% and the remaining at a loss of 25%. What is his overall percentage of gain or loss

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23. A man sells an article at a profit of 20%. If he had bought it at 10% less and sold it for Rs.18 more, he would have gained 40%. Find the cost price of the article.

1) Rs.500 2) Rs.300 3) Rs.400 4) Rs.550

24. An article was sold at a profit of 20%. If both cost price and selling price are Rs.100 less each, then magnitude of the percentage of profit would have been 4 percentage points more than that in the first case. Then the cost price is

25. A man bought 2 articles at the same price and sells them together at 30% gain. Had he bought the first article at 20% less and the second article at 10% more and then sold them together for Rs.48 less, he would have gained 20% on the whole. What is the total cost of 2 articles?

1) Rs.200 2) Rs.300 3) Rs.400 4) Rs.500

26. A trader marks up the price of the product by 40%. If the discount is increased from 15% to 25%, his profit comes down by Rs.42. What is the cost price?

1) Rs.150 2) Rs.200 3) Rs.250 4) Rs.300

27. The catalogue price of an article is Rs.15,000. If the discount is increased from 15% to 20%, then profit falls from 27.5% to 20%. Find the cost price of the

article?

1) Rs.12,000 2) Rs.10,000 3) Rs.12,250 4) Rs.12,750

28. The marked price of an article is Rs.300. If the selling price is 50% more than the amount of discount allowed, find the selling price

1) Rs.180 2) Rs.150 3) Rs.200 4) Rs.175

29. The cost of an apple is 331_/₃_{% less than the cost of 1 mango. If a man sells four}

apples at the cost price of 5 mangoes, what is his percentage of profit?

1) 75% 2) 81% 3) 87.5% 4) 90%

30. A merchant professed to sell 20 articles at a loss which is equals to the cost price of 2 articles but sold 18 articles at the cost price of 20 articles. What is the gain percent?

1) 191_/₁₁_% _{2) 10%} _{3) 11}1_/₉_% _{4) 0%}

31. The percentage by which the marked price exceeds the cost price of an article and the percentage of discount allowed on the article are in the ratio of 3:2. If it is sold at the cost price, what is the percentage of discount allowed?

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1) 20% 2) 25% 3) 331_/₃_% _{4) 50%}

32. The purchase prices of three articles are in the ratio 3:4:5 the first one is sold at a profit of 10% and the second at a loss of 7.5%. If the overall percentage of profit or loss of the first two articles is the same as the percentage profit or loss of all the articles taken together, what is the percentage of profit or loss in the case of the third article?

1) 8.75 2) 1.25 3) 0 4) Can‟t be determined.

33. A dishonest oil merchant claims that he gets a profit of only 5% but he gives only one litre of oil instead of 1kg. If 1.25 litre of oil weighs 1kg what is his overall percentage of profit?

1) 31.25% 2) 25% 3) 26% 4) None of these

34. A fruit vendor sells mangoes and bananas and gets equal revenue from each. He gets a profit of 20% on each mango and a profit of 25% on each banana. If the ratio of the number of bananas sold to the number of mangoes sold is 4:1, what is the ratio of the cost price of a banana to that of a mango?

1) 1:5 2) 6:25 3) 2:9 4) Can‟t be determined.

35. A trader buys 150 pens for Rs.1,000 and he marks each of them at Rs.10. He gives a discount of 20% on each pen and he gives 1 pen free on bulk purchases of 9 pens. What is his minimum possible overall percentage of profit?

1) 8% 2) 10% 3) 20% 4) 5%

36. A trader gives a discount on an article such that the profit as a percent of marked price is the same as the discount as a percent of cost price. What is the ratio of the actual profit percentage to the actual discount percentage an the article?

1) 4:1 2) 2:1 3) 1:2 4) Can‟t be determined.

37. The cost price of a computer is Rs.1,000 less then the selling price of a television and the selling price of the computer is 30% more than the cost price of the

television. If the selling price of the computer is 4% more than the selling price of the television, what is the percentage of profit on selling the television?

1) 20% 2) 25% 3) 162_/_3% _{4) Can‟t be determined.}

38. The marked prices of two articles are in the ratio of 1:2, their discount

percentages are also in the ratio of 1:2 and the profit they get is also in the ratio of 1:2. What is the ratio of their cost price?

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1) 1:2 2) 5:8 3) 2:5 4) Can‟t be determined. 39. A trader purchases two watches. He marks the first one up by Rs.200 over the

cost price and gives a discount of 20% on it. The second one he marks up by 50% and gives a discount of Rs.160. If he gains 15% on both the watches put together and 8% on the first alone, what is the percentage of profit on the second watch?

1) 21% 2) 22% 3) 18.5% 4) Can‟t be determined.

40. Javed sells 2,000 mangoes in a week. He recovers his total cost by selling first 1,200 Mangoes. He sells the next 300 Mangoes for a loss of 20% and he sells the last 500 Mangoes for a loss of 40%. What is his overall percentage of profit?

1) 45% 2) 35% 3) 27% 4) 12.5%

Solutions:

1. Profit at a price = loss at other price => CP must be numerically between those prices

 CP = (56+42)/2 = Rs. 49. 2. Gain % = 1000/880 => 1. 1363 => 13.63%

3. For P, SP=1080 and loss=10% => CP = 1080/0.9 =1200 => loss = 1200-1080 = 120.

For Q, SP=1800 and loss=10% => CP = 1800/0.9 = 2000 => loss = 2000-1800 = 200.

4. She got profit => profit % = 15/10 X 12/12 = 1.5 => 50%. 5. Profit % = 19 1/21 => 1.19047.

Let he measure x cm for 100 cm. Then, 100/x = 1.19047 => x=84 cm

So he measures 16 cm less for every meter. 6. Loss = 30% on CP i.e., 0.3CP => SP = 0.7CP

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Loss % on SP = loss/SP X 100 = 0.3CP/0.7CP X 100 = 42.85%.

7. Total CP = 90000 & total SP = 93000 => gain = SP/CP = 93000/90000 =1.0333 = 3.33%

8. Total cost of a watch = 180 + (500/100) = 185. Gain = 20% => SP = 1.2CP = 1.2 X 185 = 222 9. 0.75 MP = 0.8 CP (since 20% loss) So, MP = 1.0666CP => 6.66% gain 10. 1.2 X 1.25 X 0.6666 X CP = 1000 => CP = 1000 (profits of 20%, 25% & loss of 33.33%) 11. Total CP=18000+1800 = 19800.

Depreciation = 9.09% and gain = 11.11% => SP = (0.9091)X(1.1111)X19800 = 20000.

12. Let „f‟ be the factor of discount => 1000 X f X f X f = 729 => f = 0.9 => 10% decrease.

13. CP/5 = SP/6 => SP/CP=1.2 => 20% gain.

14. In two transactions B is gaining => SP > CP for B in two transactions.

So, gain% = 12/9 X 12/9 = 1.7777 => 77.77%.

15. 2 articles free for every 10 articles bought. So 10 free articles => 50 articles bought.

Money of 60 articles (10 articles free) is obtained by selling only 10 articles.

So SP of 10 articles = CP of 60 articles => SP/CP = 6 => 500% gain. 16. Total CP = 45000. Depreciation = 20% =>new CP = 0.8 X 45000 =

36000.

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17. CP => 6 apples for Rs. 10. SP => 4 apples for Rs. 10 => 6 apples for Rs. 15 So, for 6 apples, gain is Rs.5 => Rs. 60 gain requires 72 apples.

18. CP of 5 kg ghee = 300. Loss = 10% => SP = 0.9 CP = 270. For Rs. 270, 4 kg are sold

 SP for 1 kg = 270/4 =Rs. 67.5

19. Let w be the weight of the second stone.

Now, 0.9 X (1000/800) X (1000/w) = 1.0285 (since profit is 2.85%)

 w = 900 gm (nearly)

20. SP = 39. Profit % = CP.

CP + (CP% of CP) = SP => CP = 30/-.

21. ratio = 3:4 => investments are 3/7 and 4/7.

Overall loss/gain % = (3/7)(-10) + (4/7)(20) = 50/7 = 7 1/7 %.

22. 3/5th_{are sold at gain of 25% and 2/5}th_{are sold at loss of 25%.}

First, (3/5 X 25 – 2/5 X 25) = 5% gain. 23. 20% gain => SP = 1.2 CP.

New CP = 0.9 CP and New SP = SP + 18 => 1.2CP+18.

40% gain => new SP = 1.4 X new CP => (1.2CP+18) = 1.4(0.9CP) => CP = 300.

24. 20% gain => SP = 1.2CP.

New CP = CP – 100 and new SP = SP -100 & 24% gain => new SP=1.4 X new CP

 CP – 100 = 1.4 ( 1.2CP – 100) => CP = 600.

25. Let each article costs x => Total CP = 2x and SP = 1.3 X 2x = 2.6x. New total CP = 0.8x + 1.1x = 1.9x, New SP = SP – 48 = 2.6x – 48 and gain = 20% So, 2.6x – 48 = 1.2 X 1.9x => 2x = 300.

26. MP = 1.4CP. Also 10% change is discount => Rs. 42 gain => 10% of 1.4CP = 42

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 CP = 300.

27. MP = 15000. 5% change in discount i.e., 5% of MP = 7.5 % of CP (profit change)

So, CP = 5/7.5 X MP = 10000.

28. MP = 300. SP = 1.5 X discount. Now, SP = MP – discount => SP = 180. 29. CP of apple = 0.6666 X CP of mango…….1

Man sold 4 apples for CP of 5 mangoes => his CP = 4 X CP of apple And his SP = 5 X CP of mango.

So, SP/CP = (5XCP of mango)/(4XCP of apple) = 1.875 => 87.5%. 30. SP of 18 articles = CP of 20 articles => SP/CP = 20/18 = 1.1111 =>

11.11% gain

31. If CP is raised by 3x %, the discount should be 2x %. Also, after discount SP=CP => increase of 3x% X decrease of 2x%.

From inspection, 33.33% discount => 50% increase (since 3:2) and 1.5 X 0.6666 = 1.

32. CP of first two articles are in ration of 3:4.

So for 2 articles, gain/loss % = (3/7)X10 – (4/7)X7.5 = 0.

So, overall profit/loss% = 0 => (3/12)X10 – (4/12)X7.5 + (5/12)x = 0 => x=0%. 33. Overall profit = 1.05 X (1.25/1) = 1.3125 => 31.25% gain

34. For mango, SP = 1.2 CPm and for banana SP = 1.25 CPb.

Revenue from mango = revenue from banana => 1.2 CPm = 4 X 1.25 CPb (since they are sold in ratio of 1:4)

So, CPb/CPm = 6:25.

35. 150 pens for Rs.1000 => total CP = 1000.

1 pen free for every 9 pens => he can sell 135 pens (for least possible profit) SP of each pen = 10 and discount = 20% => SP = 8.

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Total SP = 135 X 8 = 1080 => SP/CP = 1080/1000 = 1.08 => 8%.

36. Profit% of MP = discount% of CP => profit%/discount% cant be determined without the values of MP and CP.

37. CP computer = SP TV – 1000 and SP computer = 1.3 X CP TV.

SP Computer = 1.04 SP TV => 1.3 CP TV = 1.04 SP TV => SP/CP = 1.25 => 25% gain.

38. Without the knowledge of atleast on of the prices the ratio of CP‟s cant be determined.

39. MP1 = CP1 + 200 and discount = 20%.Also MP2 = 1.5CP2 and discount = Rs. 160.

Also SP1/CP1 = 8% gain. With this information it can‟t be said what is the profit % on 2nd_watch.

40. 300 sold at loss of 20% and 500 old at a loss of 40% => loss% = (3/8)X20 + (5/8)X40

= 32.5 => loss factor = 0.675

Already he got a gain by SP of 1200 = CP of 2000.

So overall profit % = (2000/1200) X 0.675 = 1.125 => 12.5% gain.

Averages and Ages

What is average?

The concept of average is equal distribution of the overall value among all the things or persons present there. So the formula for finding the average is as follows:

Average, A = Total of all things, T / Number of things, N Therefore, Total, T = AN

If any person joins a group with more value than the average of the group then the overall average increases. This is because the value in excess than the average will also be distributed equally among all the members.

Similarly when any value less than the average joins the group the overall group decreases as the deficit is divided equally among all the people present there.

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Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. If another person D joins them with Rs. 50/- then he has Rs. 40/- more than actual average of Rs. 10/-.

So this Rs. 40/- will get distributed among those four and each gets Rs. 10/-. Thus the average becomes Rs. 20/- each.

Example:

The average age of a class of 30 students is 12. If the teacher is also included the average becomes 13 years. Find the teacher‟s age.

Soln:

When the teacher is included there are totally 31 members in the class and the average is increased by 1 year. This means that everyone got 1 extra year after distributing the extra years of the teacher. So extra years of the teacher are as follow: 31x1=31 years.

Age of the teacher = actual avg + extra years = 12 + 31 = 43 years.

Exercise:

1. The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven papers is 35. Find the marks obtained in the 7th_paper?

(A) 23 (B) 38 (C) 19

(D) None of these

2. The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of the players is 27 and that of another set of 5 players, totally different from the first five, is 29. If it is the captain who was not included in either of these two groups, then find the age of the captain.

(A) 75 (B) 55 (C) 50

(D) Cannot be determined

3. A bus goes to Ranchi from Patna at the rate of 60 km per hour. Another bus leaves Ranchi for Patna at the same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys of the two buses combined if it is known that the distance from Ranchi to Patna is 420 kilometers.

(A) 64.615 kmph (B) 64.5 kmph (C) 63.823 kmph (D) 64.82 kmph

4. A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire journey.

(A) 72 km/h (B) 18 km/h (C) 77.33 km/h (D) 78.5 km/h

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5. The average weight of 6 men is 68.5 kg. If I is known that Ram and Tram weigh 60 kg each, find the average weight of the others.

(A) 72.75 kg (B) 75 kg (C) 78 kg

(D) None of these

6. The average score of a class of 40 students is 52. What will be the average score of the rest of the students if the average score of 10 of the students is 61.

(A) 50 (B) 47 (C) 48 (D) 49

7. The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 years. What will be the new average if we include the 20 faculty members whose average age is 37 years?

(A) 32 years (B) 24 years (C) 25 years (D) None of these

8. Out of the three numbers, the first is twice the second and three times the third. The average of the three numbers is 88. The smallest number is

(A) 72 (B) 36 (C) 42 (D) 48

9. The sum of three numbers is 98. If the ratio between the first and second is 2 : 3 and that between the second and the third is 5 : 8, then the second number is

(A) 30 (B) 20 (C) 58 (D) 48

10. The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is

(A) 158 cm (B) 158.5 cm (C) 159 cm (D) 157 cm

11. The average weight of 6 persons is increased by 2.5 kg when one of them whose weight is 50 kg is replaced by a new man. The weight of the new man is

(A) i_{65 kg}

(B) 75 kg (C) 76 kg (D) 60 kg

12. The average age of A, B C and D five years ago was 45 years. By including X, the present average age of all the five is 49 years. The present age of X is

(A) 64 years (B) 48 years (C) 45 years (D) 40 years

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13. The average salary of 20 workers in an office is Rs. 1900 per month. If the manager‟s salary is added, the average salary becomes Rs. 2000 per month. What is the manager‟s annual salary? (A) Rs. 24, 000

(B) Rs. 25,200 (C) Rs. 45,600 (D) None of these

14. The average weight of a class of 40 students is 40 kg. If the weight of the teacher be included, the average weight increases by 500 gm. The weight of the teacher is

(A) 40.5 kg (B) 60 kg (C) 62 kg (D) 60.5 kg

15. In a Infosys test, a student scores 2 marks for every correct answer and loses 0.5 marks for every wrong answer. A student attempts all the 100 questions and scores 120 marks. The number of questions he answered correctly was

(A) 50 (B) 45 (C) 60 (D) 68

16. The average of the first ten natural numbers is (A) 5

(B) 5.5 (C) 6.5 (D) 6

17. The average of the first ten whole numbers is (A) 4.5

(B) 5 (C) 5.5 (D) 4

18. The average of the first ten even numbers is (A) 18

(B) 22 (C) 9 (D) 11

19. The average weight of a class of 30 students is 40 kg. If, however, the weight of the teacher is included, the average become 41 kg. The weight of the teacher is

(A) 31 kg (B) 62 kg (C) 71 kg (D) 70 kg

20. 30 oranges and 75 apples were purchased for Rs. 510. If the price per apple was Rs. 2, then the average price of oranges was

(A) Rs. 12 (B) Rs. 14 (C) Rs. 10 (D) Rs. 15

21. A batsman made an average of 40 runs in 4 innings, but in the fifth inning, he was out on zero. What is the average after fifth innings?

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(A) 32 (B) 22 (C) 38 (D) 49

22. The average weight of a school of 40 teachers is 80 kg. If, however, the weight of the principle be included, the average decreases by 1 kg. What is the weight of the principal?

(A) 109 kg (B) 29 kg (C) 39 kg

(D) None of these

23. The average age of Ram and Shyam is 20 years. Their average age 5 years hence will be (A) 25 years

(B) 22 years (C) 21 years (D) 20 years

24. The average of 20 results is 30 and that of 30 more results is 20. For all the results taken together, the average is

(A) 25 (B) 50 (C) 12 (D) 24

25. The average of 5 consecutive numbers is 18. The highest of these numbers will be (A) 24

(B) 18 (C) 20 (D) 22

26. Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average of the family is the same today. What is the age of the baby?

(A) 1 years (B) 2 years (C) 6 months (D) 9 months

27. Varun average daily expenditure is Rs. 10 during May, Rs. 14 during June and Rs. 15 during July. His approximate daily expenditure for the 3 months is

(A) Rs. 13 approximately (B) Rs. 12

(C) Rs. 12 approximately (D) Rs. 10

28. A ship sails out to a mark at the rate of 15 km per hour and sails back at the rate of 20 km/h. What is its average rate of sailing?

(A) 16.85 km (B) 17.14 km (C) 17.85 km (D) 18 km

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29. The average temperature on Monday, Tuesday and Wednesday was 41 0_{C and on Tuesday,}

Wednesday and Thursday it was 40 0_{C. If on Thursday it was exactly 39}0_{C, then on Monday, the}

temperature was (A) 42 0_C

(B) 46 0_C

(C) 23 0_C

(D) 26 0_C

30. The average of 20 results is 30 out of which the first 10 results are having an average of 10. The average of the rest 10 results is

(A) 50 (B) 40 (C) 20 (D) 25

31. ten years ago, Mohan was thrice as old as Ram was but 10 years hence, he will be only twice as old. Find Mohan‟s present age.

a) 60 years b) 80 years c) 70 years d) 76 years

32. The ages of Ram and Shyam differ by 16 years. Six years ago, Mohan‟s age was thrice as that of Ram‟s, find their present ages.

a) 14 years, 30 years b) 12 years, 28 years c) 16 years, 34 years d) 18 years, 38 years

33. 15 years hence, Rohit will be just four times as old as he was 15 years ago. How old is Rohit at present?

a) 20 b) 25 c) 30 d) 35

34. A man‟s age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?

a) 45 years b) 50 years c) 55 years d) 60 years

35. If twice the son‟s age in years be added to the father‟s age, the sum is 70 and if twice the father‟s age is added to the son‟s age, the sum is 95. Father‟s age is

a) 40 years b) 35 years c) 42 years d) 45years

36. Three years ago, the average age of a family of 5 members was 17. A baby having been born the average age of the family is the same today? What is the age of the child?

a) 3 years b) 5 years c) 2years d) 1 year

37. The ratio of A‟s and B‟s ages is 4:5 If the difference between the present age of A and the age of B 5 years hence is 3, then what is the total of present ages of A and B?

a) 68 years b) 72 years

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c) 76 years d) 64 years

38. The ages of A and B are in the ratio of 6:5 and sum of their ages is 44 years. The ratio of their ages after 8 years will be

a) 4 : 5 b) 3 : 4 c) 3 : 7 d) 8 : 7

39. 5 years ago, the combined age of my mother and mine was 40 years. Now, the ratio of our age is 4:1. How old is my mother?

(A) 10 (B) 40 (C) 60 (D) 20 (E) 50

40. Honey was twice as old as Vani 10 years ago. How old is Vani today if Honey will be 40 years old 10 years hence? a) 20 b) 25 c) 15 d) 35 e) 30

41. One year ago, a mother was 4 times older to her son. After 6 years, her age become more than double her son‟s age by 5 years. The present ratio of their age will be?

a.13 : 12 b.11 : 13 c.3 : 1 d.25 : 7 e.4 : 3

42. Vandana‟s mother is twice as old as her brother. She is 5 years younger to her brother but 3 years older to her sister. If her sister is 12 years of age, how old is her mother?

a.30 b.35 c.45 d.40 e.50

43. Sonu is 4 years younger Manu while Dolly is four years younger to Sumit but 1/5 times as old as Sonu. If Sumit is eight years old, how many times as old is Manu as Dolly?

a.3 b.½ c.2 d.1 e.¼

44. Our mother is 3 times as old as my brother and I am 1/3rd_{times older than my brother. If 4}

years ago I was as old as my brother today, what is the age of my mother. a.40

b.36 c.44 d.42 e.48

45. Ruchi‟s age was double that of Niti 2 years ago. If Ruchi was 2 years older to Niti then, try to guess how old she is today.

a.6 b.4 c.8 d.2 e.20

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46. If we add the age of three brothers Sunil, Sanjay and Sonu, then it becomes 60 years today. If 6 years ago the Sonu was of half the age of Sanjay and 1/3rd_{to the age of Sunil, then find out the}

present age of Sanjay. a.14

b.15 c.16 d.18 e.24

47. Sonu‟s age is 2/3rd_{of Manu‟s. After 5 years Sonu will be 45 years old. Manu‟s present age is}

a.55 b.56 c.58 d.60 e.64

48. Ratio of Sonu‟s age to Manu‟s is equal to 4:3. If Sonu will be 26 years old after 6 years, the present age of Manu is

a.11 b. 15 c.14 d.17 e.13

49. Binny is born on 1st_{October. He is younger to Sunny by one week and two days. If on 1}st_October

it was a Saturday, then Sunny‟s birthday will come on which day this year?

(A) Wednesday (B) Thursday (C) Monday

(D) Saturday (E) Sunday

50. Binny is half as old as Sunny. Chinky is twice old as Sunny. How many times is Chinky as old as Binny?

(A) 6 (B) 4 (C) 8

(D) 3 (E) 2

Ratios and Proportions

What is a ratio?

A ratio is a representation of distribution of a value present among the persons present and is shown as follows:

If a total is divided among A, B and C such that A got 4 parts, B got 5 parts and C got 6 parts then it is represented in ratio as A:B:C = 4:5:6.

So, 4:5:6 means that the total value is divided into 4+5+6 = 15 equal parts and then distributed as per the ratio.

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Divide Rs. 580 between A and B in the ratio of 14:15.

Soln:

A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20. So A‟s share = 14 parts = 14 x 20 = Rs. 280

B‟s share = 15 parts = Rs. 300.

Example 2:

If A:B = 2:3 and B:C = 4:5 then find A:B:C.

Soln:

To combine two ratios the proportions common for them shall be in equal parts. Here the common proportion is B for the given ratios.

Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15.

Example 3:

Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the three numbers.

Soln:

Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65. So the numbers are 3x = 195, 4x = 260 and 8x = 520.

Example 4:

Two numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find the numbers.

Soln:

Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given). So the numbers are 4x = 96 and 5x = 120.

Example 5:

Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 : 6. Find two numbers.

Soln:

Let the numbers be a and b. A:B = 3:4 => A / B = 3 / 4. Also, (A+8) / (B+8) = 5 / 6. Solving we get, A=12 and B = 16

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A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join the group. For how many more days will the provisions last?

Soln:

Actually after 180 days,

If 120 members are there provisions come for 60 more days (since total 240 days) But now 180 members are there.

So number of days = (120/180) X 60 = 40 days.

Example 7:

If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?

Soln:

24 men – 12 hrs – 16 days 8 men – 6 hrs - ? days (n)

n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)

=> n = 96 days.

EXERCISE

1. Divide Rs.1870 into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal.

1. 241, 343, 245 2. 400, 800, 670 3. 470, 640, 1160 4.

None

2. Divide Rs.500 among A, B, C and D so that A and B together get thrice as much as C and D together, B gets four times of what C gets and C gets 1.5 times as much as D. Now the amount C gets?

1. 300 2. 75 3. 125 4. None

3. If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day, for how many hours a day would 2 examiners have to work in order to examine twice the number of answer books in 20 days.

1. 6 2. 1/2 3. 8 4. 9

4. In a mixture of 40 liters, the ratio of milk and water is 4:1. How much water much be added to this mixture so that the ratio of milk and water becomes 2:3

1. 20 litres 2. 32 litres 3. 40 litres 4. 30 litres

5. If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is:

(42)

6. The ratio between two numbers is 3:4 and their LCM is 180. the first number is:

1. 60 2. 45 3. 15 4. 20

7. A and B are tow alloys of argentums and brass prepared by mixing metals in proportions 7:2 and 7:11 respectively. If equal quantities of the two alloys are melted to form a third alloy C, the proportion of argentums and brass in C will be:

1. 5:9 2. 5:7 3. 7:5 4. 9:5

8. If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work?

1. 24 days 2. 22.5 days 3. 30 days 4. 45 days

9. The incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3. If each saves Rs.1000, then, A‟s income is

1. 3000/- 2. 4000/- 3. 6000/- 4. 9000/-

10. If the ratio of sines of angles of a triangle is 1:1:2, then the ratio of square of the greatest side to sum of the squares of other two sides is

1. 3:4 2. 2:1 3. 1:1 4. Can‟t say

11. Divide Rs.680 among A, B and C such that A gets 2/3 of what B gets and B gets 1/4th_{of what}

C gets. Now the share of C is?

1. 480/- 2. 300/- 3. 420/- 4.

None

12. A, B, C enter into a partnership. A contributes one-third of the whole capital while B contributes as much as A and C together contribute. If the profit at the end of the year is Rs.84, 000, how much would each received?

1. 24,000, 20,000, 40,000 2. 28,000, 42,000, 14,000 3. 28,000, 42,000, 10,000 4. 28,000, 14,000, 42,000

13. The students in three batches at AMS Careers are in the ratio 2:3:5. If 20 students are increased in each batch, the ratio changes to 4:5:7. the total number of students in the three batches before the increases were

1. 10 2. 90 3. 100 4. 150

14. The speeds of three cars are in the ratio 2:3:4. The ratio between the times taken by these cars to travel the same distance is

1. 2:3:4 2. 4:3:2 3. 4:3:6 4.

6:4:3

15. Rs.2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6th_of

Amar‟s share, 1/4th_{of Bijoy‟s share and 2/5}th_{of Chandra‟s share are equal. Find Amar‟s}

share.

1. 720/- 2.1080/- 3. 450/- 4.

(43)

16. After an increment of 7 in both the numerator and denominator, a fraction changes to ¾. Find the original fraction.

1. 5/12 2. 7/9 3. 2/5 4. 3/8

17. The difference between two positive numbers is 10 and the ratio between them is 5:3. Find the product of the two numbers.

1. 375 2. 175 3. 275 4. 125

18. If 30 oxen can plough 1/7th_{of a field in 2 days, how many days will 18 oxen take to do the}

remaining work?

1. 30 days 2. 20 days 3. 15 days 4. 18 days

19. A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

1. 11:15 2. 15:11 3. 16:15 4.

15:16

20. The present ratio of ages of A and B is 4:5. 18 years ago, this ratio was 11:16. Find the sum total of their present ages.

1. 90 years 2. 105 years 3. 110 years 4. 80 years

21. Three men rent a farm for Rs.7000 per annum. A puts 110 cows in the farm for 3 months, B puts 110 cows for 6 months and C puts 440 cows for 3 months. What percentage of the total expenditure should A pay?

1. 20% 2. 14.28% 3. 16.66% 4. 11.01%

22. 10 students can do a job in 8 days, but on the starting day, two of them informed that they are not coming. By what fraction will the number of day required for doing the whole work get increased?

1. 4/5 2. 3/8 3. 3/4 4. 1/4

23. A dishonest milkman mixed 1 liter of water for every 3 liters of milk and thus make up 36 liters of milk. If he now adds 15 liters of milk to the mixture, find the ratio of milk and water in the new mixture.

1. 12:5 2. 14:3 3. 7:2 4. 9:4

24. Rs.3000 is distributed among A, B and C such that A gets 2/3rd_{of what B and C together get}

and C gets ½ of what A and B together get. Find C‟s share

1. 750/- 2. 1000/- 3. 800/- 4. 1200/-

25. If the ratio of the ages of Maya and Chhaya is 6:5 at present, and fifteen years from now, the ratio will get changed to 9:8, then find Maya‟s present age.

1. 24 years 2. 30 years 3. 18 years 4. 33 years

26. If Rs.58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?

1. 52 2. 54 3. 68 4. 62

(44)

27. If 391 bananas were distributed among three monkeys in the ratio ½:2/3:3/4, how many bananas did the first monkey get?

1. 102 2. 108 3. 112 4. 104

28. A mixture contains milk and water in the ratio 5:1. On adding 5 liters of water, the ratio of milk to water becomes 5:2. the quantity of milk in the mixture is:

1. 16 litres 2. 25 litres 3. 32.5 litres 4. 22.75 litres

29. A beggar had ten paise, twenty paise and one rupee coins in the ratio 10:17:7 respectively at the end of day. If that day he earned a total of Rs.57, how many twenty paise coins did he have?

1. 114 2. 171 3. 95 4. 85

30. Vijay has coins of the denomination of Re.1, 50 p and 25 p in the ratio of 12:10:7. The total worth of the coins he has is Rs.75. Find the number of 25 p coins that Vijay has

1. 48 2. 72 3. 60 4. None

Comprehensive Test – I

(Chapters 1 – 4)

1. 25% of a number subtracted form itself gives 120. The number is a. 125 b. 135 c. 140 d. 160 2. If x is 80 % of y, then what % of x is y? a. 20 b. 90 c. 120 d. 125

3. A man spends 30% of his income on rent, 20% on food, 20% on miscellaneous items and saves Rs. 1050. His total salary is

a. 3740 b. 3750 c. 3500 d. 3510

4. A‟s income is 25% less than that of B. By what % is B‟s income more than that of A?

a. 75 b. 25

(45)

c. 33.33 d. 66

5. In an election 10 % of the votes were invalid. 40% of the votes were for A and the rest to B. B won with a majority of 243 votes, the total number of votes polled is

a. 1250 b. 1350 c. 1155 d. None

6. In a class there were 80 boys and 70 girls. If 25% of boys and 30% of girls passed in an exam find the fail % of the class.

a. 27 b. 72.66 c. 27.5 d. 72.5

7. A person‟s salary was increased by 25% in one year. In the next year it increased by 50%. What is the % increase in the salary?

a. 87.5 b. 75 c. 37.5 d. None

8. A man scores 42.5% and failed by 5 marks in an exam. If he scored 52.5% he would pass by 15 marks. Find the minimum marks to pass.

a. 200 b. 100 c. 90 d. 80

9. A trader bought some oranges. 4% of them were spoiled, 10% of remaining rotten and he sold 90 % of the good ones. If 540 oranges were left the number of oranges he bought was

a. 6000 b. 6250 c. 6500 d. 6750

10. The population of a city was 9000. If the male population increased by 15% and the female population increased by 16% the total population

increased by 1390. The number of men were a. 4000

b. 4250 c. 4750 d. 5000

(46)

11. By selling an article for Rs. 1000 the person loses 20%. At what price it has to be sold to gain 30%?

a. 1500 b. 1625 c. 1675 d. 1680

12. SP of 4 articles is equal to CP of 3 articles. The % of gain or loss is a. 25

b. 50 c. 75 d. 80

13. A man bought 60 apples for Rs. 100 and 40 other apples for Rs. 50. How many apples has he to sell for Rs. 120 to gain 25%?

a. 10 b. 64 c. 88 d. 90

14. X sold 3/5th_{of his goods at 50 % gain. If he sells the remaining at CP}

find the overall profit %. a. 10

b. 25 c. 30 d. 40

15. A radio was sold for 18% profit. If it were sold for Rs. 30 more a profit of 20% would have gained. Find the CP.

a. 1000 b. 1200 c. 1500 d. 1800

16. A shopkeeper had calculated profit % on SP and announced it as 40%. His actual profit % is

a. 60 b. 66.5 c. 66.66 d. 66.33

17. The price of an article increased by 20% and later decreased by 20%. If present value is Rs. 480 the original price is

a. 480 b. 490 c. 500 d. 520

(47)

18. Due to increase in price of eggs by 20% two eggs less were available for Rs. 20. The present price of eggs per dozen is

a. 24 b. 20 c. 25 d. 18

19. After two successive discounts on list price of Rs. 5000 an article was sold for Rs. 3600. If the first discount was 20% the second discount is a. 5%

b. 10% c. 15% d. 20%

20. Kiran bought a radio on 15% discount. If he got a discount of 18% he would save Rs. 63. The SP is

a. 1785 b. 1722 c. 1745 d. 1740

21. A shopkeeper buys toffees at rate of 40 for Rs. 5 and sells at rate of 50 for Rs. 10. The profit % is

a. 60 b. 50 c. 25 d. 30

22. A man sells his articles at 5% above CP. If he had bought them for 5% lesser price and sold them for Rs. 2 less, he wiuld have gained 10%. The CP of the articles is

a. 500 b. 360 c. 425 d. 400

23. The marked price of a table is Rs. 1200, 20% above CP. It is sold at a discount of 10%. The profit % is

a. 10 b. 8 c. 7.5 d. 6

24. The average monthly salary of 20 employes is Rs. 1500. If the manager‟s salary is added the average becomes Rs. 1600. The manager‟s salary is

a. 3500 b. 3600 c. 3800

208666617 Total Book Rough

Manual for Corporate Recruitment

Contents

Preface

Recruitment Patterns of various MNC’s

Importance of aptitude in recruitment process

What is aptitude?

Why aptitude?

QUANTITATIVE

APTITUDE

Percentages

Exercise:

Averages and Ages

Ratios and Proportions

Comprehensive Test – I

(Chapters 1 – 4)