Question : A certain number of men can do a piece of work in 40 days. If there were 45 men more the work could have been finished in 25 days. Find the original number of men employed in the work.
Option 1: 70
Option 2: 85
Option 3: 65
Option 4: 75
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Correct Answer: 75
Solution :
Let the total number of men be $x$.
The work is the same. So, $W_1=W_2=1$
Use the following formula to solve the question:
$\frac{M_{1}\times D_{1}}{W_{1}}=\frac{M_{2}\times D_{2}}{W_{2}}$
Where $M_1$ and $M_2$ are men, $D_1$ and $D_2$ are days and $W_1$ and $W_2$ are work done.
$\frac{x×40}{1} = \frac{(x+45)×25}{1}$ ([If $x$ men are initially employed]
$⇒ 40x = 25x-1125$
$⇒ 15x= 1125$
$\therefore x = 75$
Hence, the correct answer is 75.
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