Time and Work Basics

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

M1x D1x T1x W2  =  M2x D2x T2 xW1

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 we get 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 percentage3

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

Effeciency = 100/n%

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      Work/Day                        Efficiency (%)
N                                                                                  1/n                                      100/n
1                                                                                   1                                          100
2                                                                                  1/2                                         50
3                                                                                  1/3                                        33.33
4                                                                                  1/4                                          25
5                                                                                  1/5                                          20
6                                                                                  1/6                                         16.66
7                                                                                  1/7                                         14.28
8                                                                                  1/8                                          12.5
9                                                                                  1/9                                         11.11
10                                                                               1/10                                         10
11                                                                               1/11                                         9.09
12                                                                               1/12                                       8.25
13                                                                               1/13                                         7.69
14                                                                               1/14                                       7.14

15                                                                               1/15                                        6.66