Catching up to a wall-length target with added manpower A 1000-meter wall must be built in 50 days. 56 men are hired, but after 27 days only 448 meters are completed. How many additional men must be employed to finish the remaining work on time?

Introduction / Context:
This is a throughput calibration question. We infer the per-man productivity from the initial phase, then size the workforce needed to hit the deadline for the remaining work.

Given Data / Assumptions:

• Total wall length = 1000 m; deadline = 50 days.
• Initial crew = 56 men for 27 days; output = 448 m.
• Assume constant per-man productivity throughout.

Concept / Approach:
Compute per-man rate from realized output, then compute how many men are needed to complete the remaining meters in the remaining days. Finally subtract current men to get “additional men.”

Step-by-Step Solution:

Verification / Alternative check:
Check capacity: 81 men for 23 days at 8/27 gives 81 * 23 * 8/27 = 552 m remaining, so the target is hit exactly.

Why Other Options Are Wrong:
23, 27, 31 do not equal the computed increment from 56 to 81; any other total misses 552 m in 23 days.

Common Pitfalls:
Using the planned average rate (20 m/day) instead of inferring the true p from realized output.

Final Answer:
25