A contract must be finished in 92 days by 234 men working 16 hours per day. After 66 days, 4/7 of the work is completed. If each man now works 18 hours per day, how many additional men are needed to finish on time?

Introduction / Context:Varying daily hours changes throughput, so compute in man-hours. From the completed fraction, determine the remaining man-hours and solve for the headcount at the new hours to meet the deadline.

Given Data / Assumptions:

• Initial setup: 234 men, 16 h/day, 92 days planned.
• After 66 days → completed 4/7.
• Remaining days: 92 - 66 = 26; new hours = 18 h/day.

Concept / Approach:Let W be total man-hours. Use 66-day production to infer W, then compute men M such that M * 18 * 26 equals remaining 3/7 W. Subtract current 234 to get additional men.

Step-by-Step Solution:

Verification / Alternative check:Dimensional check in man-hours confirms units and cancellation are consistent.

Why Other Options Are Wrong:They do not satisfy the precise balance of remaining man-hours within 26 days at 18 h/day.

Common Pitfalls:Using man-days instead of man-hours after changing daily hours.

Final Answer:162