Question

A contractor undertook to complete a project in 90 days and employed 60 men on it. After 60 days, he found that $\frac{3}{4}$ of the work has already been completed. How many men can he discharge so that the project may be completed on time ?

• A. 15
• B. 20
• C. 25
• D. 30

Answer 1

The correct option is B 20

$\frac{3}{4}th$ of the work is completed by 60 men in 60 days $\frac{3}{4}$ of the work is completed by 1 man in (60 x 60) days

$\therefore$ The whole work will be completed 1 man in $(60\times 60\times \frac{4}{3})$ days

Let the number of men who can complete the remaining $\frac{1}{4}$ of the work in remaining 30 days be $x$.

Then, $\frac{1}{4}th$ of the work will be completed by x men in 30 days.

$\frac{1}{4}th$ of the work will be completed by 1 man in $\left(30x\right)$ days

$\therefore$ The work will be completed by 1 man in (X x 30 x 4) days

$\therefore 60\times 60\times \frac{4}{3}=x\times 30\times 4\Rightarrow x=40$

$\therefore$ Number of men who can be discharged $=60-40=20$