A contract is to be completed in 50 days with 105 men working 8 hours per day. After 25 days, only 2/5 of the work is finished. If each man now works 9 hours per day, how many additional men are required to complete the work on time?

Introduction / Context:When hours per day change mid-project, treat work in man-hours. Use completed fraction to infer total work, then determine the remaining workforce at new hours to meet the deadline.

Given Data / Assumptions:

• Initial: 105 men, 8 h/day, 25 days → completed 2/5.
• Remaining time: 50 - 25 = 25 days at 9 h/day.

Concept / Approach:Work W in man-hours. Compute W from the 2/5 completion, then solve M such that M*9*25 equals remaining 3/5 of W.

Step-by-Step Solution:

Verification / Alternative check:Check: 140*9*25 = 31500 → matches remaining workload.

Why Other Options Are Wrong:Off-by-one choices (34, 36, 37) test arithmetic; only 35 satisfies the exact equality.

Common Pitfalls:Forgetting to convert to man-hours after changing the daily hours.

Final Answer:35