Staggered workforce: 25 men can reap a field in 20 days. After working some days with all 25, 15 men leave and the remaining 10 must finish in 37.5 days. After how many days should 15 men leave?

Introduction / Context:
Break total work into two phases with different workforce sizes. Compute total job in man-days from the baseline, then equate it to the sum of man-days delivered in phase 1 (25 men for x days) and phase 2 (10 men for 37.5 days) to solve for x.

Given Data / Assumptions:

• 25 men finish in 20 days ⇒ total work = 25 * 20 = 500 man-days.
• Phase 1: 25 men for x days.
• Phase 2: 10 men for 37.5 days (after 15 leave).

Concept / Approach:
Total man-days supplied must equal the job’s 500 man-days. Hence 25x + 10*37.5 = 500. Solve for x to find when the reduction should occur to still finish on time.

Step-by-Step Solution:

Verification / Alternative check:
Man-days supplied = 25*5 + 10*37.5 = 125 + 375 = 500; equals the job size, confirming the timing.

Why Other Options Are Wrong:
10, 9, 7, 6 days give totals other than 500 man-days and therefore miss the required completion in 37.5 days overall.

Common Pitfalls:
Trying to average days or workers instead of using man-day equality across phases.

Final Answer:
After 5 days