Aptitude questions all topics (1)

Manual for Aptitude
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Manual for Aptitude
Contents
I. Preface
1. Why this book?
2. What does it contain?
II. Selection Procedures of MNC’s
III. Importance of Aptitude in Recruitment Process
IV. Patterns of various MNC Aptitude Papers
V. Quantitative Aptitude
1. Percentages
a. Percentage change
b. Percentage difference
c. Multiple percentage changes
2. Profit & Loss
a. Discounts
b. % Profit
c. % Loss
3. Averages and Ages
4. Ratios and Proportions
a. Partnerships
b. Mixtures & Allegations
5. Test on chapters 1 to 4
6. Solutions for the test
7. Time and Distance
a. Trains
b. Boats & Streams
c. Races
8. Time and Work
a. Work & Wages
b. Pipes & Cisterns
9. Mensuration
a. Areas
b. Volumes
c. Basics of Geometry
12. Interest
a. Simple Interest
b. Compound Interest
13. Clocks
14. Calendars
15. Probability
a. Playing Cards
b. Dices
c. Coloured Balls

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VI. Logical Aptitude
1. Blood Relations
2. Directions
3. Coding & Decoding
4. Series
a. Letter Series
b. Number Series
c. Odd Man Out Series
5. Analytical Reasoning
a. Arrangements
b. Comparisons
c. Selections
d. Family Based Problems
e. Intersection Type
6. Critical Reasoning
7. Cubes
a. Counting the cubes
b. Painting with equal cuttings
c. Painting with inequal cuttings
d. Miscellaneous
8. Logical Deductions
9. Data Interpretation
10. Data Sufficiency
11. Venn Diagrams
VII. Verbal Aptitude
1. Reading Comprehension
2. Vocabulary Test
3. Sentence Completion
a. Prepositions
b. Adverbs
c. Conjunctions
d. Verb Forms
4. Sentence Correction

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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 themprepare 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 I can
guarantee that 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.
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 themwith
all the inputs and guiding themtowards their placement in the companies.

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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:
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 neverget a chance to prove any otherexpertise you possess in other
aspects.
This is the reason why aptitude is considered the most important factor by the aspirants of various MNC recruitments.

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Importance of Aptitude
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 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.
Aptitude is a language – Speak it.
Aptitude is eternal – Don’t make it material.
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 uniformplatformfor 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%?
Soln: 35% = 35/100 = 0.35.
For faster calculations we can convert the percentages ordecimal 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

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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
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 less 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.

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Eg: By what percent is 40 more than 30?
Soln: % difference = (40-30)/30 X 100 = 33.33%
(Here 40 is compared with 30. So 30 is taken as denominator)
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.
Eg: When the actual value is x, find the value when it is 30% decreased.
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)

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 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 of10% 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?
a. 100 b. 200 c. 300 d. None
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

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11. A reduction of 10% in price of sugarenables 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 salt and water with 20% salt, 2lt of water is evaporated.Find the new % concentration of salt.
a. 20% b. 23% c. 25% d. None
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 shopkeeperoffers three successive discounts of10%, 20% and 30% to a customer. If the actual price of the item is
Rs. 10000, find the price the customer 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 shorterthan 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?
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
So, new savings = 1.2I – 1.04I = 0.16I => 16%
(So income decreased form 20% to 16%)
% decrease = (20-16)/20 X 100 = 20%.
7. It is equivalent to 1.25 decreased to 1.

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% 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 of20%, 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.
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%)
(OR) 60 out of 80 is 3/4. So, (3/4 X 75) + (1/4 X x) = 80 => x =95.

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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 fromthe business
is called Selling Price.
In other words, Selling Price is nothing but the returns froma 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.
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.

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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.
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 2nd 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.
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 themat 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 s old 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%.
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:

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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 anotherarticle 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?
1) 30% 2) 20% 3) 15% 4) None of these
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) 331/3%
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 scooterfor 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 91/11% 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 overa 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 ofthe 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) 142/7%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
1) 777/9% 2) 75% 3) 50% 4) 662/3%
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) 121/12% 3) 161/4% 4) 111/9%
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

Manual for Aptitude
16
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) 71/7% 3) 111/9% 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
1) 5% loss 2) 10% gain 3) 5% gain 4) No loss, No gain
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 togetherat 30% gain. Had he bought the first article at 20%
less and the second article at 10% more and then sold them togetherfor 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) 111/9% 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?
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 of9 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?

Manual for Aptitude
17
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?
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
Loss % on SP = loss/SPX 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.
SP = 40000 => SP/CP = 40/36 = 1.1111 => 11.11% gain
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 2/5th are sold at loss of 25%.

Manual for Aptitude
18
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
 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.
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.

Manual for Aptitude
19
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.
Example:
Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. If anotherperson 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 s even 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 fromRanchi to Patna is 420 kilometers.
(A) 64.615 kmph (B) 64.5 kmph (C) 63.823 kmph (D) 64.82 kmph

Manual for Aptitude
20
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
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) 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
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
11

Manual for Aptitude
21
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?
(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 approx (B) Rs. 12 (C) Rs. 12 approx (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
29. The average temperature on Monday,Tuesday and Wednesday was 41 0C and on Tuesday,Wednesday and Thursday it
was 40 0C. If on Thursday it was exactly 39 0 C, then on Monday, the temperature was
(A) 42 0C (B) 46 0C (C) 23 0C (D) 26 0C
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 (B) 12 , 28 (C) 16 , 34 (D) 18 , 38
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?
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?
38. The ages of A and B are in the ratio of 6:5 and sumof 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
(B) 50

Manual for Aptitude
22
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 youngerto 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 youngerto 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 howold she is
today.
a.6 b.4 c.8 d.2 e.20
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 youngerto Sunny by one week and two days.If on 1st 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

Manual for Aptitude
23
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.
Example 1:
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 sumof 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.

Manual for Aptitude
24
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
Example 6:
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 togetherget 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 sumis 18, then the ratio of squares of the numbers is:

Manual for Aptitude
25
1. 6:12:13 2. 1:2:4 3. 36:144:324 4. None
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 togethercontribute. 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 ofthree 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 2/5th of Chandra’s share are equal. Find Amar’s share.
1. 720/- 2.1080/- 3. 450/- 4. 1240/-
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%

Manual for Aptitude
26
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 togetherget and C gets ½ of what
A and B togetherget. 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
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
5

Manual for Aptitude
27
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 (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
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 shopkeeperhad 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 original price is
a. 480 (B) 490 (C) 500 (D) 520
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 discountson 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 shopkeeperbuys toffees at rate of 40 for Rs. 5 and sells at rate of 50 for Rs. 10. The profit % is

Manual for Aptitude
28
a. 60 (B) 50 (C) 25 (D) 30
22. A man sells his articles at 5% above CP. If he had bought themfor 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 (D) 3900
25. Of the three numbers the first is twice the second and half of the third. Their average is 56. Find the smallest
number.
a. 20 (B) 22 (C) 24 (D) 26
26. A batsman scores 64 runs in his 16th innings and increases his average by 3. His average after 16th innings is
a. 18 (B) 17 (C) 19 (D) 16
27. 12 yrs ago, the average age of a husband and his wife was 20yrs. The average age is same today,they having two
children. What is the present age of the youngest child if children differ in age by 2yrs?
a. 6 (B) 5 (C) 8 (D) 7
28. The average age of jawans in army of 40 is reduced by 1yr when 10 men with average 20 yrs are replaced by 10
new men. Find the average age of the new men?
a. 14 (B) 15 (C) 16 (D) 17
29. The average weight of 8men in increased by 2 kg when one of them with weight of 50kg is replaced by a new
man. The weight of the new man is
a. 60 (B) 65 (C) 63 (D) 66
30. The average age of husband,wife and their child 3yrs ago was 27yrs and that of the wife and the child 5yrs ago
was 20yrs. The present age of the husband is
a. 40 (B) 30 (C) 33 (D) 43

Manual for Aptitude
29
Time and Distance
Speed:
We have the relation between speed,time and distance as follows:
Speed = distance / time.
So the distance covered in unit time is called speed.
This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or
Time = Distance / Speed.
Units of Speed:
The units of speed are kmph (km per hour) or m / s.
1 kmph = 5 / 18 m / s
1 m / s = 18 / 5 kmph
Average Speed:
When the travel comprises of various speeds then the concept of average speed is to be applied.
Average Speed = Total distance covered / Total time of travel
Note: In the total time above,the time of rest is not considered.
Example 1:
If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph find its average speed.
Soln:
Average Speed = Total distance / Total time.
Let each side of square be x km. Then the total distance = 4x km.
The total time is sum of individual times taken to cover each side.
To cover x km at 100 kmph, time = x / 100.
For the second side time = x / 200.
Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph.
Example 2:
A man if travels at 5/6 th of his actual speed takes 10 min more to travel a distance.Find his usualtime.
Soln:
Let s be the actual speed and t be the actual time of the man.

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30
Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same.
So distance 1 = distance 2 => s X t = (5/6)s X (t+10) => t = 50 min.
Example 3:
If a person walks at 30 kmph he is 10 min late to his office. If he travels at 40 kmph then he reaches to his office 5 min
early. Find the distance to his office.
Soln:
Let the distance to his office be d. The difference between the two timings is given as 15 min = 1 / 4 hr.
Now if d km are covered at 30 kmph then time = d/30. Similarly second time = d/40.
So, d/30 – d/40 = 1 / 4 => d = 30 km.
Note:
When two objects move with speeds s1and s2
a. In opposite directions their combined speed = s1 + s2
b. In same direction their combined speed = s1 ~ s2.
Example 4:
Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite directions. Find the
distance between them after 3 hrs.
Soln:
Speed = 30 + 40 = 70 kmph (since in opposite directions)
Time = 3 hrs
So distance = speed X time = 70 X 3 = 210 km.
Example 5:
A starts from X to Y at 6 am at 40 kmph and at the same time B starts from Y to X at 50 kmph. When will they meet if X
and Y are 360 km apart?
Soln:
Distance = 360 km
Speed = 40 + 50 = 90 kmph.
Time = distance / speed = 360 / 90 = 4hrs from 6 am => 10 am.
Example 6:
A starts from X to Y at 6 am at a speed of 50 kmph. After two hours B starts from Y to X at 60 kmph. When will they meet
if X and Y are 430 km apart?
Soln:
By the time B started A traveled for 2 hrs => 2 X 50 = 100 km.
So at 8 am, distance = 430 – 100 = 330 km

Manual for Aptitude
31
Speed = 50 + 60 = 110 kmph.
Time = distance / speed = 330 / 110 = 3 hrs from 8 am => 11 am.
Note:
When a train crosses a negligible length object (man / pole / tree) the distance that it has to travel is its own length.
When a train has to cross a lengthy object (train / bridge / platform) the distance it has to travel is the sumof its length and
the length of the object.
Example 7:
If a train traveling at 40 kmph crosses anothertrain of length 100m traveling at 14 kmph in opposite direction in 30 s find
the length of the train.
Soln:
Let length of train be d.
Distance to be covered = d + 100.
Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s
Time = 30 s.
Distance = speed X time => d+100 = 15 X 30 => d = 350 m.
Note:
If a man rows a boat along the stream flowing at speed S2 then it is termed downstreamspeed and is given by
S down = S1 + S2 , where S1 is speed of boat in still water.
If a man rows a boat opposite to the stream flowing at S2 then it is termed upstreamand is given by
S up = S1 – S2.
Exercise:
1. A car moves at a speed of 80km/hr. What is the speed of the car in meters per second?
1)
9
2
12 2)
9
2
22 3)
9
1
20 4)
2
9
21
2. If a man can cover 12 meters in one second,how many kilo meters can be cover in 3 hours 45 minutes?
1) 168 km 2) 162 km 3) 150 km 4) 156 km
3. If a man running at 15 kmph. Crosses a bridge in 5 minutes, then the length of the bridge is
1) 1230 m 2) 1240 m 3) 1250 m 4) 1220 m
4. Walking at
th
4
3
of his usualspeed a man is late by 2 hours 30 minutes. The usual time would have been
1)
2
1
7 hrs 2)
2
1
3 hrs 3)
4
1
3 hrs 4)
8
7
hrs
5. In a 1 km race, A beats B by 100 m and C by 150 m. In a 2700 m race, by how many meters does B beat C?
1) 100 m 2) 120 m 3) 150 m 4) 180 m
6. Traveling at a speed of 8 kmph a student reaches schoolfrom his house 10 minutes early. If he travels at 6
kmph, he is late by 20 minutes. Find the distance between the schooland the house.
1) 12 km 2) 1 km 3) 10 km 4) 13 km
7. A man takes 5 hours 45 minutes in walking to a certain place and riding back. He could have gained 2 hours
by riding both ways. The time he would take to walk both ways is _________
1) 12 hrs 2) 11 hrs 45minutes 3) 7 hrs 45 minutes 4) 3 hrs

Manual for Aptitude
32
8. The ratio between rates of walking of two persons is 3:4. If the time taken by nd
2 person to cover a certain
distance is 36 minutes, then the time taken by the first person to cover the same distance is ___________
1) 36 minutes 2) 48 minutes 3) 27 minutes 4) none
9. If the speed of a vehicle changes in the ratio a : b, then the ratio of times taken is
1) a : b 2)
1b
a
3) b : a 4)
1a
b
10. A car driver makes his journey by the speed of 75km/hr and returns to initial place with 50 km/hr. Then his
average speed of journey is ___________
1) 30 km/hr 2) 40 km/hr 3) 50 km/hr 4) 60 km/hr
11. A vehicle travels 715 km at a uniform speed.If the speed of the car is 10 kmph more, it takes 2 hours less to
cover the same distance. The original speed was _______________
1) 45 kmph 2) 65 kmph 3) 55 kmph 4) 75 kmph
12. Two persons P and Q run at 8 kmph and 12 kmph on a circular track of length 6 km in the same direction
starting at same time from same place. After how many hours will they meet each other any where on the
track?
1) 1.5 hours 2) 2 hours 3) 2.5 hours 4) 3.5 hours
13. A car driver driving at a speed of 68kmph locates a truck 40 meters ahead of him. After 10 seconds,the truck
is 60 meters behind. The speed of truck is ____________
1) 30 km/hr 2) 32 km/hr 3) 23 km/hr 4) 3 km/hr
14. Rajan is traveling on his cycle and has calculated to reach a point at 2 p.m. if he travels at 10 kmph. He would
reach there by 12 noon if he travels at 15 kmph. At what speed must he travel to reach the same place at
1.p.m?
15. Two persons start running simultaneously around a circular track of length 300m from the same point at
speeds 15 and 25km/hr. When will they meet first time on the track, when move in opposite direction?
1) 21 sec 2) 22 sec 3) 27 sec 4) 24 sec
16. A robber steals a Maruthi car at 2.30 pm and drives at 60 kmph. The theft is discovered at 3 p.m. and the
owner sits in Police jeep running at 75 kmph. When will he catch the thief?
1) 5.30 pm 2) 5.15 pm 3) 5 pm 4) 5.45 pm
17. Two planes move along a circle of circumference 1.2 km with constant speeds.When they move in different
directions they meet every 15 sec and then they move in the same direction one plane over takes the other
every 60 sec.The speed of slower plane is
1) 0.04 km/s 2) 0.03 km/s 3) 0.05 km/s 4) 0.02 km/s
18. A 150 m long train crosses a man walking at a speed of 6 kmph in his opposite direction in 6 sec. The train (in
kmph) is:
1) 66 2) 84 3) 96 4) 106
19. A train of length 150 m takes 10 sec to pass over anothertrain 100 m long coming from the opposite direction.
If the speed of the train is 30 kmph. Then the speed of the second train in kmph is _________
1) 54 2) 60 3) 72 4) 36
20. If a train 110m long passes a signal pole in 3 sec. Then the time taken by it to cross a railway platform 165m
long is :
1) 3secs 2) 4secs 3) 7.5secs 4) 5secs
21. An Engine of 10 m length travels at 60 kmph. How long does it take to cross anothertrain 170 m long,
running at 54 kmph in the same direction?
1) 16 sec 2) 16.8 sec 3) 108 sec 4) none
22. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross
each other at a distance of 110 km from one of the stations.What is the ratio of their speeds?
1) 9:11 2) 11:9 3) 10:9 4) 9:10
23. A train M leaves Mumbai at 5am. And reaches Delhi at 9am. Anothertrain leaves Delhi at 7am. And reaches
Mumbai at 11.00am. At what time do the two trains across each other?
1) 8 a.m. 2) 9 a.m. 3) 7 a.m. 4) 6 a.m.
24. Train P leaves Hyderabad at 6.00am. And reaches Vijayawada at 10.00am. Train Q leaves Vijayawada at
7.00am. And reaches Hyderabad at 1.00pm. At what time do the trains meet?
1) 8.48 a.m. 2) 8.12 a.m. 3) 8.42 a.m. 4) 9.00 a.m.
25. A train running at 52kmph takes 36 seconds to pass a platform. Next it takes 24 seconds to pass a man
walking at 10 kmph in the same direction. Find the length of the train and that of the platform?
1) 800 m; 440 m 2) 280 m; 440 m 3) 280 m; 240 m 4) 420 m; 300 m

Manual for Aptitude
33
26. Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 60 seconds.
If the length of the first train is 125 meters, then the length of second train is?
1) 125 m 2) 128 m 3) 175 m 4) 900 m
27. Two trains 220 meters and 380 meters in length respectively are running in opposite direction. One at the rate
of 35 kmph and other at 25 kmph. In what time they will cross each other?
1) 36 seconds 2) 30 seconds 3) 60 seconds 4) None
28. A man misses a train by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the
train by 10minutes. What is the minimum speed required to catch the train on time?
29. A boat traveled from A to B and back to A from B in 5 hours.If the speed of boat in still water and the speed
of stream be 7.5 kmph and 1.5 kmph, then what is the distance between A and B?
1) 80 km 2) 45 km 3) 18 km 4) 19 km
30. A man can row downstream at 18 kmph and upstreamat 10 kmph. Find the speed of the man in still water and
the speed of stream (in kmph)
1) 13; 3 2) 15; 3 3) 12; 6 4) 14; 4
31. A man can row at 9 kmph in still water. He takes 4 ½ hours to row from P to Q and back. What is the
distance between P and Q if the speed of the stream is 1 kmph?
1) 32 km 2) 28 km 3) 20km 4) 24 km
32. A man can row 30 km downstream in 3 hours 45 minutes, and 11 km upstreamin 2 hours 12 minutes. What is
the speed of the man in still water and speed of stream (in kmph)?
1) 6; 2 2) 6.8; 1.8 3) 6.5; 1.5 4) 7; 3
33. A man rows 22 km upstreamin 4 hours and 45 km downstream in 6 hours. In 10 hours how much more
distance can he row downstreamthan the distance he can row upstream?
1) 24 km 2) 22 km 3) 20 km 4) 18 km
34. A person can row 10 km in 1 hourin still water. If the speed of the water current is 2 kmph and it takes two
hours for him to go to a certain place and back. Find the distance he traveled in upstream?
1) 9 ½ km 2) 9.6 km 3) 48 km 4) 5 km
35. A person can row
5
3
of a km in upstreamin 10 minutes and return in 6 minutes. Find the speed of man in still
water?
1) 4.4 kmph 2) 4.5 kmph 3) 4.8 kmph 4) 4.9 kmph
36. A boat can travel 10 kmph in still water. It traveled 91 km downstream and then returned, taking altogether20
hours.Find speed of the stream?
37. The time taken for a boat to cover certain distance in upstreamis equal to the time taken by the boat to cover
three times the distance in downstream. If the speed of current is 5 kmph, what is the speed of boat in still
water?
38. The time taken by a person to row upstreamis twice the time taken by him to row the same distance
downstream. If the speed of the boat in still water is 42 kmph, find the speed of current?
39. A man rows his boat to a certain place covering a distance of 72 km and back again in 15 hours. He finds that
he takes same time to row 3 km in downstream as much he takes for 2 km in upstream. Find the speed of the
stream?
40. A man can row 6 km/hr in still water. If the speed of stream is 2km/hr, it takes him 3 hours to row to a place
and back. How far is the place?
1) 16 km 2) 10 km 3) 12 km 4) 8 km

Manual for Aptitude
34
Time and Work
If a person can complete a work in ‘n’ days then he can do 1/n part of the work in one day.
The amount of work done be a person in 1 day is called his efficiency.
Example:
A can do a work in 10 days.Then the efficiency of A is given by A = 1 / 10.
Note:
Number of days required to do a work = work to be done / work per day.
Example 1:
If A can do a work in 10 days,B can do it in 20 days and C in 30 days in how many days will the three togetherdo
it?
Soln:
The efficiencies are A = 1/10, B = 1/20 and C = 1/30
So work done per day by the three = 1/10 + 1/20 + 1/30 = 11/60 => No of days = 60/11 = 5.45 days.
Example 2:
If A and B can do a work in 10 days , B and C can do it in 20 days and C and A can do it in 40 days in what time all
the three can do it?
Soln:
A+B = 1/10
B+C = 1/20
C+A = 1/40
Adding all the three we get 2(A+B+C) = 7/40 => A+B+C = 7/80 => No of days = 80/7 days.
Note:
If all the people do not work for all the time then the principle below can be used:
mA + nB + oC = 1. (1 is the total work)
Here, m=no of days A worked
n=no of days B worked
o=no of days C worked
A,B,C = efficiencies
Example 3:
If A can do a work in 12 days,B can do it in 18 days and C in 24 days.All the three started the work. A left after two
days and C left three days before the completion of the work. How many days are required to complete th e work?

Manual for Aptitude
35
Soln:
Let the total no of days be x.
A worked only for 2 days,B worked for x days and C worked for x-3 days.
So, mA + nB + oC = 1
 2(1/12) + x(1/18) + (x-3)(1/24) = 1
 12 + 4x + 3(x-3) = 72
 x = 69 / 7 days.
Note:
The ratio of dividing wages = ratio of efficiencies = ratio of parts of work done
Example 4:
A can do a work in 10 days and B can do it in 30 days and C in 60 days.If the total wages for the work is Rs. 1800
what is the share of A?
Soln:
Ratio of wages = 1/10 : 1/30 : 1/60 = 6 : 2 : 1 (Multiplying each term by LCM 60)
So total 9 equal parts in Rs. 1800 => each part = Rs. 200 => share of A = 6 parts = Rs. 1200.
Note:
When pipes are used filling the tank they are treated similar to the men working but some outlet pipes emptying the
tank are present whose work will be considered negative.
Example 5:
A pipe can fill a tank in 5 hrs but because of a leak a the bottomit takes 1 hr extra. In what time can the leak alone
empty the tank?
Soln:
Let the filling pipe be A.
A = 1 / 5.
But with the leak L, A – L = 1 / 6 ( A-L because leak is outlet)
So, 1/L = 1 / 5 – 1/ 6 = 1/30 => Leak can empty the tank in 30 hrs.
Example 6:
A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All are opened at the same time.
After how many hours shall the pipe B be closed such that the tank can be filled in 10 hrs?
Soln:
Let the pipe B be closed after x hrs.
Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs.
mA + nB – oC = 1 (since C is outlet)

Manual for Aptitude
36
10(1/10) + x(1/20) – 10(1/40) = 1
x = 5 hrs.
Exercise:
1. A alone can complete the work in 12 days while A and B togethercan complete the same work in 8 days.The
number of days that B will take to complete the work alone is ___________
1) 10 2) 24 3) 20 4) 9
2. A can do a work in 6 days and B in 9 days.How many days will both take togetherto complete the work.
1) 7.5 2) 5.4 3) 3.6 4) 3
3. A can do a piece of work in 4 hours,B and C can do it in 3hrs, A and C can do it in 2hrs. How long will B alone
take to do it?
1) 10hrs 2) 12hrs 3) 8hrs 4) 24hrs
4. 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days.In how many
days will a woman finish the work?
1) 125 2) 150 3) 90 4) 225
5. A completes a work in 12 days; B completes the some work in 15 days.A started working alone and after 3 days
B joined him. How many days will they now take togetherto complete the remaining work?
1) 5 2) 8 3) 6 4) 4
6. 10 men can complete a piece of work in 15 days & 15 women can complete the same work in 12 days.If all the
10 men & 15 women work together,in how many days will the work get completed?
1) 6 2)
3
2
7 3)
3
2
6 4) None of these
7. A can do a certain work in the same time in which B & C togethercan do it. If A and B togethercould do it in
10 days and C alone in 50 days then B alone could do the work in
1) 15 days 2) 20 days 3) 25 days 4) 30 days
8. A& B undertook to do a piece of work for Rs.4,500. A alone could do it in 8 days and B alone in 12 days.With
the assistance ofC they finished the work in 4 days.Then C’s share of the money is ____________
1) Rs.2,250 2) Rs.1,500 3) Rs.750 4) Rs.375
9. A can finish a work in 24 days,B in 9 days and C in 12 days.B & C start the work but are forced to leave after 3
days.The remaining work is done by A in _____________
1) 5 days 2) 6 days 3) 10 days 4)
2
1
10 days
10. If 3 men (or) 4 women can plough a field in43 days,how long will 7 men and 5 women take to plough it.
11. A can do
th
4
3
of a work in 12 days.In how many days can he finish
th
8
1
of work?
1) 1 day 2) 2 days 3) 4 days 4) 8 days
12. If 72 men can build a wall 280m. long in 21 days,how many men will take 18 days to build a similar type of
wall of length 100m.?
1) 30 2) 10 3) 18 4) 28
13. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together,they
can finish the work in 2 days.B can do the work alone in
14. A does
5
4
of a piece of work in 20 days; he then calls in B and they finish the remaining work in 3 days. How
long will B alone take to do the whole work?
1)
2
1
37 days 2) 37 days 3) 40 days 4) 23 days
15. A does half as much work as B in 1/6 of the time. If togetherthey take 10 days to complete a work, how many
days shall B take to do it alone?
16. A man, a woman and a boy can togethercomplete a piece of work in 3 days. If a man alone can do it in 6 days
and a boy alone can do it in 18 days,how long will a woman alone take to complete the work.

Manual for Aptitude
37
17. If the wages of 6 men for 15 days be Rs.700, then the wages of 9 men for 12 days will be ___________
1) Rs.700 2) Rs.840 3) Rs.1050 4) Rs.900
18. A man is paid Rs.20 for each day he works, and forfeits Rs.3 for each day he is idle. At the end of 60 days he
gets Rs.280. Then he was idle for _____________
19. A team of 10 men can complete a particular job in 12 days.A team of 10 women can complete the same job in 6
days.How many days are needed to complete the job if the two teams work together?
1) 4 2) 6 3) 9 4) 18
20. A contractorundertook to finish a certain work in 124 days and employed 120 men on it. After 64 days,he
found that he had already done
rd
3
2
of the work. How many men he can discharge now so that the work may
finish in time
1) 24 2) 56 3) 64 4) 80
21. A work could be completed in 100 days.However, due to the absence of 10 workers, it was completed in 110
days.The original number of workers was ___________
1) 100 2) 110 3) 55 4) 50
22. A contractorunder takes to make a road in 40 days and employs 25 men. After 24 days,he finds that only one-
third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days
earlier?
1) 100 2) 60 3) 75 4) none of these
23. 30 men complete one third of a work in 30 days.How many more men should be employed to finish the rest of
the work in 40 more days?
1) 15 2) 45 3) 20 4) 25
24. A and B under took to do a piece of work for Rs.900. A alone could do it in 60 days and B in 30 days.If A & B
work togetherand complete the work, then the share of B _______
1) Rs.600 2) Rs.400 3) Rs.300 4) Rs.200
25. 5 men or 6 women or 10 boys can do a work in 15 days.How long will it take to complete the work by a group
of 5 men, 6 women and 10 boys?
26. A can do a piece of work in 30 days.B in 15 days and C in 10 days.They started the work all togetherbut B put
2
1
time daily and C put
3
1
time daily to help A in doing the work. The work will last in ______________
27. A can do a work in 15 days & B the same work in 12 days.B started the work and was joined by A, 5 days
before the end of work. The work lasted for _____ days.
1) 8 2) 12 3) 13 4) 24
28. A and B can do a piece of work in 40 days while C & A can do it in 60 days.If B is twice as good as C, then C
alone will do the work in ___________ days.
1) 120 2) 100 3) 80 4) 24
29. A hostelhas provision for 800 men for 24 days at the rate of 2 kg per man per day. For how many men is the
provision sufficient, for 20 days at the rate of 1.5 kg per man per day?
1) 1280 2) 1000 3) 1820 4) 1240
30. 12 men can do a work in 15 days working 8 hours a day. In how many days can 9 men do the same work,
working 10 hours a day?
1) 10 2) 16 3) 18 4) 24
31. Two taps A and B can separately fill a tank in 20 and 30 hours respectively. If both the pipes are opened
simultaneously, how much time will be taken to fill the tank?
1) 10 hrs 2) 11 hrs 3) 18 hrs 4) 12 hrs
32. A tap can fill a tank in 12 minutes and anothertap in 15 minutes, but a third tap can empty it in 6 minutes. The
three taps are kept open together.Find when the cistern is emptied or filled?
1) 60 min. to fill 2) 30 min. to fill 3) 60 min to empty 4) 30 min to empty
33. Two taps A & B can fill a cistern in 12 and 16 minutes respectively. Both fill taps are opened together, but 4
minutes before cistern is full, one tap A is closed.How much time will the cistern take to fill?
1) 9 1/7 min. 2) 3 1/7 min. 3) 11 1/7 min. 4) None.

Manual for Aptitude
38
34. A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 minutes. 80 tonnes would suffer
to sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing that she may just
reach the shore as she begins to sink.
1) 5.5 kmph 2) 2.5 kmph 3) 1.8 kmph 4) 4 kmph
35. A tap can fill a swimming pool in h hours.What part of the pool is filled in y hours?
1) yh 2)
y
h
3)
h
y
4) h – y
36. Three pipes A, Band C can fill a tank in 30 min, 40 min and 60 min respectively. A and B work in alternative
minutes, A beginning the work whereas C works continuously.In how many minutes will the tank be filled?
1) 16.4 2) 21.8 3) 18.2 4) 19.6
37. A tank has a leak, which would empty it in 8 hrs. A tap is turned on which admits 6 litres of water a minute into
the tank and it is now emptied in 12 hrs.How many litres does the tank hold?
1) 8640 2) 8460 3) 8064 4) 8406
38. A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its
bottom. If the cistern is full, then the leak will empty the cistern in
1) 20 hours 2) 40 hours 3) 50 hours 4) 30 hours
39. Two pipes A and B can separately fill a cistern in 60 and 75 minutes respectively. There is a third pipe at the
bottomof the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50
minutes. In how much time can third pipe alone empty the cistern?
1) 110 minutes 2) 100 minutes 3) 120 minutes 4) 90 minutes
40. A tap can fill a tank in 6 hours.After half the tank is filled, three more similar taps are opened.What is the total
time taken to fill the tank completely?
1) 4 hours 2) 4 hours 15 min 3) 3 hours 15 min 4) 3 hours 45 minutes

Manual for Aptitude
39
Mensuration
I. Triangle
(a). Any triangle
a, b and c are three sides of the triangle; h is the altitude and AC is the base.
Perimeter (P) : P = a + b + c = 2s
Area (A) : A = 
2
1
base  altitude =
2
1
 any side  length of  r dropped on that side = )cs()bs()as(s 
(b). Equilateral
a is the length of each side
Perimeter (P) : P = 3a Area (A) : A =
4
3
a2
(c). Right-angled
b, c are the lengths of the two legs
Perimeter (P) : P = a + b + c = 2s Area (A) : A = 
2
1
product of two legs
(d). Isosceles
a is the length of two equal sides
b is the base
BD is the perpendicular dropped on base such that it divides the base equally AD = CD =
2
b
Perimeter (P) : P = 2a+b Area (A) : A = 22
ba4
4
b

(e). Right-angled Isosceles
Perimeter (P) : P = 2  a  ( 2 +1) Area (A) : A = 
2
1
(a)2
II. Quadrilateral
(a). Any Quadrilateral
AC is the diagonal = d, DE and BF are two perpendicular drawn on the diagonal (AC) P1, and P2 are the lengths of the two
perpendiculars
Perimeter (P) : P = sum of the four sides.
Area (A) : A = 
2
1
d  (p1+p2)= 
2
1
any diagonal  (sum of  rs drawn on that diagonal)
(b). Rectangle
l = length
b = breadth
d = diagonal

Manual for Aptitude
40
Perimeter (P) : P = 2(l + b) = 2(l+ 22
ld  ) =2 A2d2
 Area (A): A = l b
(c). Square
a = length of side
d = diagonal
Perimeter (P) : P = 4a = 2d 2 Area (A) : A = a2 =
16
p
=
2
d 22
(d). Rhombus
a = each side
d1 = one diagonal
d2 = another diagonal
h = height
Perimeter (P) : P = 4a = 2 2
2
2
1 dd  Area (A) : A = 
2
1
d1  d2 = a  h
(e). Trapezium
a and b are two parallel sides,h is the height
Area (A) : A =
2
1
(a + b)  h =
2
1
 (sum of parallel sides)  (perpendicular distance between parallel sides)
(f). Parallelogram
b is the base
h is the perpendicular distance between the base and its opposite side
Area (A) : A = b  h = base  (perpendicular distance between the base and its opposite sides)
= 2  area of Δ ABD (or Δ BCD)
III. Polygon
Polygon is a n-sided closed figure bounded only by line segments.
In a polygon if the internal angle at each vertex is less than 180o then the polygon is a convex polygon,else a concave
polygon.
Convex Polygon:
i. Area of a regular polygon =
2
1
 perimeter  r
 distance from the center of the polygon to any side.
ii. Number of diagonals in a polygon =
2
)3n(n 
iii. Sum of all interior angles of a polygon = (2n-4)  90o
iv. Each interior angle of n-sided regular polygon = 




 
n
2n
180o
v. Sum of all exterior angles of n-sided regular polygon = 360o
vi. Each exterior angle of n-sided regular polygon =
n
360
IV. Circle
O is the center of the circle
OA = OC = OB = OD = radius of circle = r; AC = BD = diameter of circle = d = 2r
Circumference (or Perimeter) C = 2π r = π d.

Manual for Aptitude
41
Area of circle A = π r2 = π
4
d2
If C = circumference, A = area then A =
2
r
C
A
and
π4
C2

V. Sector of a circle
Area of sectorAOB = 2
o
rπ
360
θ

Length of the Arc AB = rπ2
360
θ
o

VI. Rectangular Paths
Case - I
Pathway is outside the rectangle
The length of rectangle AB = l, Breadth BC = b and , Width of path way = W, then
Area of Pathway = 2W (l+b+2w) (shaded portion)
Case – II
Path way is inside the rectangle
Area of Pathway = 2W(l+b-2W) (shaded portion)
VII. Circular Pathway
OAC is a circle of radius = r, there is pathway,outside the circle of width = W
Area of circular pathway = π  W (2r+W)
When, the pathway is inside the circle,
Area of circular pathway = π  W (2r - W)
Examples:
1. If three sides of a triangle are 5, 6 and 7 cm respectively, find the area of triangle.
Sol: Area of  = s(s a)(s b)(s c)  
Now, s =
a b c 5 6 7
2 2
   
 = 9
 Area = 9 (9 5)(9 6)(9 7) 9 4 3 2       
= 216 6 6 cm2 .
2. ABC is an equilateral triangle of side 24 cm. Find the in radius of the triangle.
Sol: In a equilateral triangle, the altitude, median and perpendicular are equal.
 AD = 3 /2 x 24 = 12 3
GD (in radius) = 1/3 x 12 3 = 4 3 cm

Manual for Aptitude
42
3. The base and other side of an isosceles triangle is 10 and 13 cm respectively. Find its area.
Sol: Area of Isosceles  = 2 2b
4a b
4

Given, base b = 10 Other side a = 13
Area (A) = 2 210 10
4 (13) 10 676 100
4 4
   
=
10
4
 24 = 60 cm2 .
4. In a right-angled triangle, the length of two legs are 12 and 5 cm. Find the length of hypotenuse and its area.
Sol: In a right angled triangle,
(Hypotenuse)2 = (one leg)2 + (other leg)2
= 122 + 52
 Hypotenuse = 2 2
12 5 = 169 = 13 cm.
In a right angled triangle,
Area = 1 2
1 1
(leg) (leg) 12 5
2 2
     = 30 cm2 .
5. If the perimeter and diagonal of a rectangle and 14 and 15 cm respectively. Find its area.
Sol: In a rectangle,
2
(Perimeter)
4
= (diagonal)2 + 2 x Area ;
2
(14)
4
= (5)2 + 2 x Area
 2 x Area =
196
4
- 25  Area =
49 25
2

= 12 cm2 .
6. Find the length of the diagonal and the perimeter of a square plot if its area is 900 square metres.
Sol: In a square, A =
2 2
d p
2 16

 (Diagonal)2 = 2 x Area = 900
 Diagonal (d) = 2 900 30 2   = 42.42 metres
(Perimeter)2 = 16 x Area = 16 x 900
 Perimeter (P) = 16 900 = 120 metres.
7. A field in the shape of a rhombus has the distances between pairs of opposite vertices as 14 m and 48 m.
What is the cost (in rupees) of fencing the field at Rs.20 per metre?
Sol: The diagonals are 14 m and 48 m
Sides of rhombus =
2 2
14 48
625
2 2
   
    
   
= 25
Perimeter of rhombus = 4 x 25 = 100 m.
Cost of fencing the field = 100 x 20 = Rs.2000

Manual for Aptitude
43
8. In a trapezium, the length of parallel sides are 20 and 25 metres respectively and the perpendicular distance
between the parallel sides is 12 metres. Find the area of trapezium.
Sol: One parallel side a = 20 metres. Second parallel side b = 25 metres. Height (perpendicular distance
between a and b) = 12 metres.
Area =
1 1
(a b) h (20 25) 12
2 2
     = 270 m2 .
9. The distance between a pair of opposite vertices of a quadrilateral is 32 units. The lengths of the
perpendiculars drawn on to this diagonal from the other two vertices are 4 1/3 units and 6 2/3 units
respectively. Find the area (in sq units) of the quadrilateral?
Sol: Area of quadrilateral = 1/2 x 32 x
13 20
3 3
 
 
 
= 178 sq units.
10.
In the above parallelogram ABCD, A = x + 30o and D = x – 40o , what is the measure of DCB ?
Sol: In a parallelogram, sum of adjacent angles is equal to 180o
 x + 30 + x – 40 = 180  x = 95o
DAB = x + 30 = 95 + 30 = 125o
 DCB = DAB = 125o
(opposite angles of a parallelogram are equal)
11. In a circle of radius 49 cm, an arc subtends an angle of 36o at the centre. Find the length of the arc and the
area of the sector.
Sol: Length of the arc =
2 r 2 22 49 36
360 7 360
θ   


= 30.8 cm
Area of the sector =
2
r 22 49 49 36
360 7 360
θ   


= 754.6 cm2
12. A rectangular plot of dimensions 13 m x 17 m is surrounded by a garden of width 5 m. What is the area (in
sq m) the garden?
Sol: Let ABCD be the rectangular plot of given dimension. The shaded part is the surrounding garden. Now,
the plot ABCD together with the garden forms another rectangular form PQRS. Dime nsions of PQRS, as can
be seen from the diagram, are:
Length PQ = width of garden + AB + width of garden
= 5 + 17 + 5 = 27 m
Similarly, breadth = PS = 5 + 13 + 5 = 23 m
Area of garden = Area of PQRS – Area of ABCD
= (27 x 23) – (17 x 13) = 621 – 221 = 440 sq m.
13. There is a rectangular field of length 100 m and breadth 40 m. A carpet of 2 m width is to be spread from the
centre of each side to the opposite side. What is the area of the carpet?
Sol: Area of the carpet ABCD = 40 m x 2 m = 80 m2
A B
DC

Manual for Aptitude
44
Area of the carpet EFGH = 100 m x 2 m = 200 m2
But the common area of two carpets = 2 x 2 = 4m2
So, area of the carpet = 200 + 80 – 4 = 276 m2
14. There is an equilateral triangle of which each side is 3 m. With all the three vertices as centres, circles w ith
radius 1.5 cm are described (i) Calculate the area common to all the circles and the triangle. (ii) Find the
area of the remaining portion of the triangle.
Sol: (i) Area of each sector = 21
r
6
  
So area common to the all the circles and triangle = 3 2 21 1
r r
6 2
     
=
1 22
1.5 1.5
2 7
   = 3.53 m2
(ii) Area of the shaded portion = Area of the triangle – Area common to the triangle and the circles
But area of the triangle = 2 23 3 9 3
a (3)
4 4 4
  m2
So area of the shaded portion =
9 3
4
m2 – 3.53 m2 = 3.89 m2 – 3.53 m2 = 0.36 m2
Exercise:
1. The base and otherside of an isosceles triangle is 10 cm and 13 cm respectively. Find its area.
1. 23 cm2 2. 60 cm2 3. 65 cm2 4. 23 cm2
2. If the area of triangle is 150 m2 and base : height is 3 : 4, find its height and base respectively.
1. 75 m, 100 m 2. 100 m, 75 m 3. 75 m, 75 m 4. None
3. Find the area of an equilateral triangle of side of 12 cm.
1. 72 sq cm 2. 36 3 sq cm 3. 12 3 sq cm 4. 18 3 sq cm
4. The height of a triangle is 8/9th of its base and its area is 576 sq cm. Find its height.
1. 36 cm 2. 52 cm 3. 72 cm 4. 32 cm
5. Find the area of a triangle whose sides are 66 cm, 88 cm and 1.1 m.
1. 2640 sq cm 2. 2904 sq cm 3. 2940 sq cm 4. 1452 sq cm
6. Area of an equilateral triangle is 16 3 sq cm, Find its perimeter.
1. 12 cm 2. 48 cm 3. 24 cm 4. 16 cm
7. What is the height of an equilateral triangle if its side is 8 3 cm?
1. 6 cm 2. 8 cm 3. 24 cm 4. 12 cm
8. In a quadrilateral, the length of its diagonals is 12 cm and the offsets drawn on this diagonal measure 13 cm and 7 cm
respectively. Find its area.
1. 546 m2 2. 273 m2 3. 60 m2 4. 120 m2
9. In a parallelogram, the lengths of adjacent sides are 11 m and 13 m respectively. If the length of one diagonal is 16
m, find the length of otherdiagonal.
1. 18 m 2. 96 m 3. 18 m 4. 40 m
10. The two adjacent sides of a parallelogram are 12 m and 14 m respectively, and if the diagonal connecting the ends is
22 m respectively, find the area of the parallelogram.
1. 151.87 m2 2. 115.78 m2 3. 151.78 m2 4. 115.87 m2
11. The base and the height of a parallelogram are 25 cm and 20 cm respectively. Find its area.
1. 500 sq cm 2. 250 sq cm 3. 45 sq cm 4. 125 sq cm
12. If the perimeter and diagonal of a rectangle and 14 cm and 5 cm respectively. Find its area.
1. 6 cm2 2. 19 cm2 3. 12 cm2 4. 9 cm2
13. The area and the perimeter of a rectangle are 84 m2 and 38 m respectively. Find its length and breadth.
1. 12 m, 7 m 2. 14 m, 6 m 3. 42 m, 19 m 4. None
14. A rectangular grass field is 112 m x 78 m. It has a gravel path 2.5 m wide all round it on the inside. Find the area of
gravel path.
1. 8736 sq m 2. 925 sq m 3. 4368 sq m 4. 952 sq m

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