Question : A contractor undertook to finish a work in 92 days and employed 110 men. After 48 days, he found that he had already done $\frac{3}{5}$ part of the work, the number of men he can withdraw so that the work may still be finished in time is:
Option 1: 45
Option 2: 40
Option 3: 35
Option 4: 30
Correct Answer: 30
Solution :
Given:
A contractor undertook to finish a work in 92 days and employed 110 men. After 48 days, he found that he had already done $\frac{3}{5}$ part of the work.
We know,
$\frac{M_{1}\times D_{1}}{W_{1}}=\frac{M_{2}\times D_{2}}{W_{2}}$
Where $M_1$ and $M_2$ are men, $D_1$ and $D_2$ are days and $W_1$ and $W_2$ are work done.
Let $n$ number of men be withdrawn.
So, $\frac{110 \times 48}{\frac{3}{5}} = \frac{(110-n) \times 44}{\frac{2}{5}}$
$⇒ 110 × 16 = (110-n) × 22$
$⇒160 = (110-n) × 2$
$⇒80 = 110-n$
$⇒n = 110 - 80$
$\therefore n = 30$
Hence, the correct answer is 30.
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