# QOTD-A is four times as good a workman as B and thus, able to finish a piece of work in 90 days less as compared to B. In how many days the work can be completed if they work together?

2019-08-07 | Team PendulumEdu

Options:

A. 24

B. 18

C. 20

D. 16

Solution:

As we know, efficiency is inversely proportional to time.

According to the question, the ratio of efficiencies of A and B is 4 : 1

Thus, the ratio of time taken by A and B alone to complete the work will be 1 : 4

Let the time taken by A to complete the work is x days

So time taken by B to complete the work will be 4x days

As given, A finishes a piece of work in 90 days less as compared to B

4x – x = 90

x = 30

So,

A alone can complete the work in 30 days.

B alone can do it in 120 days

So, 1 day work of A and B, if both are working together will be

$$\frac{1}{x}+\frac{1}{4x}=\frac{1}{30}+\frac{1}{120}$$

$$\frac{1}{24}$$

Therefore, A and B together will require 24 days to complete the work.

Hence, A is the correct answer.

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