Meeting a deadline by releasing workers: 90 men are engaged to finish a job in 40 days. After 25 days, 2/3 of the work is complete. How many men can be released so that the remaining work is finished on schedule (i.e., within the original 40 days)?

Introduction / Context:
Use the observed progress to infer per-man productivity, then compute how many are needed to finish the remainder in the remaining days. The rest can be released.

Given Data / Assumptions:

• Planned: 40 days total with 90 men.
• After 25 days, work done = 2/3.
• Remaining time = 40 − 25 = 15 days; remaining work = 1/3.

Concept / Approach:
Estimate daily team rate from progress so far, convert to per-man rate, and then deduce the required team size for the remainder.

Step-by-Step Solution:
Observed team rate = (2/3) / 25 = 2/75 per day.Per-man rate r = (2/75) / 90 = 1/3375 per day.Let N men work the last 15 days: N * r * 15 = 1/3 ⇒ N * (15/3375) = 1/3 ⇒ N/225 = 1/3 ⇒ N = 75.Men to release = 90 − 75 = 15.

Verification / Alternative check:
Check: 75 men for 15 days at 1/3375 each ⇒ 75 * 15 / 3375 = 1/3 ✔.

Why Other Options Are Wrong:
10, 20, 25, 30 would not hit exactly the remaining 1/3 in 15 days given the inferred per-man rate.

Common Pitfalls:
Assuming original planned rate instead of using actual measured progress; arithmetic slips with thirds.

Final Answer:
15