Time & Work - Concept

Time and Work is an important Cat concept which is often asked in the Cat exam. It is an easy topic if you are able to get hold on the concepts. So, let us understand the concept of Time and Work.

Work Done

The product of efficiency and time is known as work done.

Work Done = Efficiency * Time where efficiency is the rate at which work is done.

Work and Time Relation

1. If a person can complete a work in x days, then their efficiency is 1/x of the work per day.

2. If two or more people with different efficiencies, work together, there efficiency is added.

Method to solve Work Done problems

If two or more persons/machines are working on a task, then, we can use LCM of their efficiencies to simplify calculations.

Example: If A can do a job in 12 days and B can do the same job in 15 days. Then, how many days will they take, if they work together?

Answer: Take LCM of 12 and 15 => 60

A's efficiency = 60/12 = 5 units per day

B's efficiency = 60/15 = 6 units per day

(A+B)'s efficiency = 6+5 = 11 units per day

Time taken = 60/11 days

Work Done by Groups

Work Sharing

The amount of work that can be done by two people if they are working together.

If A can do a work in a days and B can do the same work in b days, then, if they work together, they can do the work in

(a*b)/(a+b) days.

Worker Replacement Problems

The problems where a worker either leaves, joins or is replaced after working for a few days.

Example: If A can do a piece of work in 10 days and B can do it in 15 days. A alone works for 5 days, then B joins. In how much days extra, will they be able to complete the work?

A's work in 5 days = 5/10 = 1/2

Work left to be done = 1/2

A and B together works => 10*15/10+15 => 6

For 1/2 work = 0.5 * 6 = 3 days

So, in 3 more days A and B together will be able to finish the work.

In the next post, we will learn more about time and work problems. I hope this concept would be clear to you all. If you have any doubts, you can ask in the comments section