Man-days held constant, compressing duration: 10 men can build a wall in 8 days. If the job must be completed in half a day (0.5 day), how many men are required, assuming everyone works at the same constant rate?

Introduction / Context:
This is a pure man-days calculation. For the same job, (men * days) remains constant if per-man productivity is constant. To reduce the number of days, the number of men must increase proportionally.

Given Data / Assumptions:

• Initial plan: 10 men * 8 days = 80 man-days of work.
• New plan: finish in 0.5 day.
• All workers have equal, constant productivity; no setup overheads.

Concept / Approach:
Let M be the required number of men for half a day. Since total work is unchanged, M * 0.5 = 80. Solve for M.

Step-by-Step Solution:
Work W = 80 man-days.Let M men work for D = 0.5 day: M * 0.5 = 80.M = 80 / 0.5 = 160 men.

Verification / Alternative check:
Cross-check with proportionality: If time is reduced by a factor of 16 (from 8 days to 0.5 day), the men required increase by the same factor: 10 * 16 = 160.

Why Other Options Are Wrong:

• 80, 100, 120 are too few; they would not supply the necessary 80 man-days within 0.5 day.

Common Pitfalls:

• Reading “half days” ambiguously; here we explicitly interpret as “half a day” to match the viable option and standard man-day logic.

Final Answer:
160