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Quantitative Aptitude Made Easy
Page 1

Quantitative Aptitude Made Easy
Index
Foreword ................................................................................... 1
Preface ....................................................................................... 3
Introduction ............................................................................... 5
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Number System
Average
LCM & HCF
Ratio & Proportion
Percentage
Partnership
Mixtures & Alligations
Simple Interest & Compound Interest
Problems Based on Ages
Profit & Loss
Sequence & Series
Time & Work
Pipes & Cisterns
Time & Distance
Boats & Streams
Calendar
Clocks
Permutation & Combination
Probability
Trigonometry
Geometry
Mensuration
Data Sufficiency
Data Interpretation
Page 2

Quantitative Aptitude Made Easy
Chapter - 12
Time and Work
Three main factors of Time and Work
There is a definite relationship between Time and Work. In this concept, there are only three factors:
Time taken to complete a certain job
Unit of work done
Number of persons doing the job
There is a mental relationship between these three, discussed as follows:
Work done (W) = Number of days (Time taken) (T or D) × Number of men (M)
W=D×M
Some basic points
More number of men can do more work i.e. both are directly proportional
More number of men take less time to complete certain job i.e. both are inversely proportional
By summarizing, we get
= ×
Let us start solving some examples:
Example 1: 10 men can cut 8 trees in 16 days. In how many days can 6 men cut 10 trees?
Solution: This is a very simple example. You are given:
W1 = 8
W2 = 10
M1 = 10
M2 = 6
D1 = 16
D2 = ?
Using formula,
= ×
=
×
⇒D2 = 33.3
Concept of efficiency
This means, "How much work one person can do in one day (expressed in percentage)"
For example: A person can do a job in 2 days
⇒ He can do 50% work in one day
Therefore, his efficiency will be 50%
Just a 2-step concept
This concept involves two steps to calculate efficiency:
Convert into fraction i.e. per day work
Multiply with 100 i.e. convert into percentage
Page 3

Quantitative Aptitude Made Easy
Try the following example first, then re-read above points
Example 2: If a person can complete his work in 5days. What will be his efficiency?
Solution: Number of days a person take to complete his work = 5
⇒ He is doing 1/5 th work per day (converted into fraction)
Convert it into percentage:
100/5 = 20%
Therefore, his efficiency is 20%.
Summarizing, If a person can do his job in n days, efficiency will be
Efficiency = %
Note: Negative efficiency cancels the positive efficiency
For Example: Positive efficiency = 5%
Negative efficiency = 1.5%
Net efficiency = 5- 1.5 = 3.5%
As we all know, in competitive exams time management is very important. I suggest you to learn the
fractions till 15.
Number of days required to
complete work
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Work/Day
Efficiency (%)
1/n
1
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11
1/12
1/13
1/14
1/15
100/n
100
50
33.33
25
20
16.66
14.28
12.5
11.11
10
9.09
8.25
7.69
7.14
6.66
Example 3: A can do a job in 10 days. B can do a job in 5 days. In how many days they can complete
the job if they work together?
Solution: Consider the above table
A's efficiency = 10%
B's efficiency = 20%
A+ B efficiency = 10 + 20 = 30%
This means, In one day A and B together can do 30% of work.
Therefore, Number of days A and B together take to do 100% of work =
⇒3.33 days
Page 4

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