Man-days scaling to a fraction of a day: 10 men can build a wall in 8 days. How many men are required to complete the same work in half a day (assume identical efficiency)?

Introduction / Context:
This uses the man-days concept with a very short target time. If the total man-days are fixed for a given job, reducing the days to a fraction requires increasing the number of men proportionally to keep the product constant.

Given Data / Assumptions:

• 10 men * 8 days = fixed work.
• All men work at the same rate.
• Target completion time = 0.5 day (half a day).

Concept / Approach:
Total man-days required = 10 * 8 = 80. Required men = total man-days / target days = 80 / 0.5.

Step-by-Step Solution:
Total man-days = 80. Men needed in 0.5 day = 80 / 0.5 = 160.

Verification / Alternative check:
Check proportionality: target time is 1/16 of 8 days; thus men must be 16 times 10, i.e., 160 men.

Why Other Options Are Wrong:
80, 100, 120 do not satisfy 80 man-days when multiplied by 0.5 day.

Common Pitfalls:
Misreading “half a day” as “half the days.” Here it explicitly means 0.5 day, not 4 days.

Final Answer:
160