Twelve men can complete a job in 24 days (constant rate and identical efficiency). If only 8 men are engaged, in how many days will the job be finished?

Introduction:
With identical workers at a constant rate, total work (in man-days) is fixed. Changing the number of men scales time inversely. We simply compute the total man-days from the first scenario and divide by the new headcount to get the new duration.

Given Data / Assumptions:

• 12 men complete the job in 24 days.
• All men are assumed identical and work at a constant pace.
• Now only 8 men will work on the same job.

Concept / Approach:
Total work W = 12 * 24 man-days. With 8 men, days needed D = W / 8. This is a direct inverse proportion of time with respect to the number of workers for fixed total work and constant efficiency.

Step-by-Step Solution:

Verification / Alternative check:
Compare ratios: time ∝ 1/men, so D_new = 24 * (12/8) = 24 * 1.5 = 36, consistent with the man-day calculation.

Why Other Options Are Wrong:
28, 48, 52, or 32 days do not preserve the constant man-days of 288 for 8 men.

Common Pitfalls:
Using direct proportion (time increasing with men) instead of inverse, or forgetting the job remains identical in scope.

Final Answer:
36