A contractor undertakes to make a tunnel in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier ?

Given:

A contractor undertakes to make a tunnel in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. He wants to complete the work 4 days earlier.

Formula used:

Work done = Number of men × Number of days

Calculation:

Let the total work be W.

Work done in 24 days by 25 men = 25 × 24

⇒ Work done in 24 days = 600 units

Given that only one-third of the work is done, so total work W = 600 × 3 = 1800 units

Remaining work = Total work - Work done = 1800 - 600 = 1200 units

Remaining days to complete work = 40 - 24 - 4 = 12 days

Let x be the number of extra men required.

Total men required to complete the remaining work in 12 days = (25 + x)

⇒ (25 + x) × 12 = 1200

⇒ 25 + x = 100

⇒ x = 75

∴ The correct answer is option 1.