# 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.

Time and Work questions are asked in quantitative aptitude section of the various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, IBPS PO, IBPS SO, IBPS RRB office assistant, IBPS RRB officer scale 1, IBPS Clerk, RBI Assistant, etc. Try and attempt free mock tests at PendulumEdu.