Question : Seventy-five men are employed to lay down a railway line in 3 months. Due to certain emergency conditions, the work be finished in 18 days. How many more men should be employed to complete the work in the desired time?
Option 1: 300
Option 2: 325
Option 3: 350
Option 4: 375
Correct Answer: 300
Solution :
Given: 75 men ($men_1$) lay down a railway line in 3 months or 3 × 30 = 90 days ($day_1$).
Let $x$ more men be employed in emergency conditions to complete the work in 18 days.
Then, the total number of men is $(75+x)$.
Now, $\frac{(Men_1×Day_1)}{Work_1} = \frac{(Men_2×Day_2)}{Work_2}$.
⇒ $\frac{(75×90)}{1} = \frac{(75+x)18}{1}$
⇒ $75×5=75+x$
⇒ $x=375-75$
⇒ $x = 300$
So, 300 more men are required to complete work in 18 days.
Hence, the correct answer is 300.
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