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

Step 1: Note what is known after 25 days.
105 men worked 25 days at 8 hours a day and finished \( \frac{2}{5} \) of the work. Days left = \(50 - 25 = 25\), work left = \(1 - \frac{2}{5} = \frac{3}{5}\), and hours per day change to 9.

Step 2: Use the men-days-hours-work relation.
The total work capacity (men times days times hours) is proportional to the fraction of work done: \[ \frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2} \]

Step 3: Plug in the known values. \[ \frac{105 \times 25 \times 8}{2/5} = \frac{M_2 \times 25 \times 9}{3/5} \]

Step 4: Simplify both sides.
Left side: \(105 \times 25 \times 8 \times \frac{5}{2} = 52500\). Right side: \(M_2 \times 25 \times 9 \times \frac{5}{3} = 375 M_2\).

Step 5: Solve for \(M_2\). \[ 375 M_2 = 52500 \] \[ M_2 = 140 \]

Step 6: Find additional men needed.
Extra men required = \(140 - 105 = 35\). Options A (34) and B (36) are close but do not satisfy the exact ratio, and D (37) overshoots. Only 35 balances the equation.

Final Answer:
35 additional men must be employed. \[ \boxed{35} \]