Changing the workforce size: 12 men can finish a piece of work in 24 days. If only 8 men are assigned, how many days will they need to complete the same work (assume equal efficiency)?

Introduction / Context:
Workload is constant and equals workers times days when all workers have equal efficiency. Decreasing the number of workers increases the required days proportionally to keep the product equal to the same total work.

Given Data / Assumptions:

• Total work W in man-days = 12 * 24 = 288 man-days.
• New team = 8 men, identical efficiency.

Concept / Approach:
Days = W / workers = 288 / 8. This directly gives the revised duration to finish the job when worker count changes and productivity per worker remains unchanged.

Step-by-Step Solution:

Verification / Alternative check:
Check proportionality: Reducing workers from 12 to 8 is a factor of 2/3; time increases by reciprocal 3/2: 24 * 1.5 = 36 days, consistent.

Why Other Options Are Wrong:
28, 48, and 52 days do not preserve the 288 man-day total; 32 is also inconsistent with the proportional scale-up.

Common Pitfalls:
Averaging or guessing instead of preserving worker-days. Always keep total man-days invariant for identical efficiency conditions.

Final Answer:
36