Twenty five men can reap a field in 20 days. If 15 men leave after some days and the field must then be finished in 37.5 days from that leaving point, after how many days should the 15 men leave?

Introduction / Context:
This staged-work problem has two phases with different team sizes. The total work remains constant, but the team rate changes after workers leave. We compute the partial work done before departure and equate the remainder to the plan after departure.

Given Data / Assumptions:

• Full job by 25 men takes 20 days.
• After some t days, 15 men leave, leaving 10 men to finish.
• From leaving time, completion must occur in 37.5 days.

Concept / Approach:
Let r be one man’s daily work. Total work W = 25 * r * 20. Before leaving: work done = 25 * r * t. After leaving: remaining work is completed by 10 men in 37.5 days, that is 10 * r * 37.5. Sum equals W.

Step-by-Step Solution:

Verification / Alternative check:
Before leaving, 25 men for 5 days do 125 man days. Remaining is 500 − 125 = 375 man days, exactly equal to 10 men for 37.5 days.

Why Other Options Are Wrong:
6, 4, 7 days do not split the work into the required 375 man days remainder after departure.

Common Pitfalls:
Interpreting 37.5 as total project time; forgetting that 37.5 is measured after the leaving moment; dropping the factor of 25t in the first phase.

Final Answer:
5 days