Question

A contract is to be completed in 50 days and 105 men were set to work, each working 8 hours a day. After 25 days, \( \frac{2}{5} \) of the work is finished. How many additional men should be employed so that the work may be completed on time, with each man now working 9 hours a day?

• A. 34
• B. 36
• C. 35
• D. 37

Hint:

Convert the finished and remaining work into total man-hours, since men times days times hours stays proportional to the fraction of work done.

Answer 1

The Correct Option is C

Instead of the combined ratio formula, work out the job in man-hour units directly.

1. Find total man-hours for the finished part: 105 men times 25 days times 8 hours = 21000 man-hours completed \( \frac{2}{5} \) of the job, so the whole job needs \( 21000 \times \frac{5}{2} = 52500 \) man-hours.
2. Find man-hours left: used man-hours = 21000, so the remaining job needs \(52500 - 21000 = 31500\) man-hours.
3. Convert remaining man-hours into men for the new schedule: 25 days remain at 9 hours a day, so hours available per man = \(25 \times 9 = 225\). Men needed = \( \frac{31500}{225} = 140 \).

Extra men to hire = \(140 - 105 = 35\), matching option C.

Let's summarize:

• Converting the job into a fixed man-hour total first, then dividing by the hours each man can give, sidesteps setting up a proportion with fractions.

Both methods agree that 35 extra men are needed.