Published: Published Date - 11:02 PM, Mon - 9 May 22

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Work topic.

TIME & 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

1. If A can do a piece of work in n days, work done by A in 1 day = 1/n
2. If A does 1/n work in a day, A can finish the work in n days
3. There is a Facts mental relationship between these three, discussed as follows:
4. Work done (W) = Number of days (Time taken) (T or) × Number of men (M)
5. 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
W1/W2 = M1/(M2 ) × D1/(D2 )

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,
W1/W2 = M1/(M2 ) × D1/(D2 )
8/10 = 10/6 × 16/𝐷2
⇒D2 = 33.3

Concept of efficiency (LCM Method):
This means, “How much work one person can do in one day”

WORK = Efficiency X Time Example: Amiit can complete a work in 10 days and Vinit can complete the work in 15 days. Then how many day both together can complete the work?
This can be understood in terms of the above example in
The following way:
Let us assume that total work to be equal to the LCM of
The days taken by Amit and Vinit (i.e., of 10 and 15)
Assume work = 60 units
Work done by Amit in one day = 5 units
Work done by Vinit in one day = 4 units
Work done by both of them in one day when working
Together = 9 units
So, the number of days taken by both of them when
Working together = 60/9 = 6 2/3days.

Example: A can finish a work in 24 days, B in 9 days and C in 12days. B & C start the work but are forced to leave after 3days. The remaining work done by A in Solution:
LCM of 24,12,9 = 72 (total work)
Find speed column (follow red arrow)
Given
B+C work for 3 days
(follow 2nd table)
So combined speed of B+C=8+6=14
D =14×3=42
Remaining work = 72-42=30
A’s speed =3
Time taken by A to do remaining work = 30/3 = 10

Banda Ravipal Reddy Director, SIGMA Sai Institute of General Mental Ability Hyderabad