Either 50 men or 80 women can finish a job in 50 days (equal total work). A contractor employs 40 men and 48 women. After every 10 days, 5 men and 8 women are removed, and this pattern continues until the job is completed. In how many days is the work finished?

Introduction / Context:We are given equivalence: 50 men or 80 women in 50 days both complete the same 1 job. Compute per-man and per-woman daily rates, then evaluate work done in successive 10-day blocks as the crew shrinks.

Given Data / Assumptions:

• Men-only plan: 50 men * 50 days = 1 job ⇒ man rate m = 1/2500 job/day.
• Women-only plan: 80 women * 50 days = 1 job ⇒ woman rate w = 1/4000 job/day.
• Initial crew: 40 men + 48 women; every 10 days remove 5 men and 8 women.

Concept / Approach:Compute each 10-day block’s crew rate and cumulative work. Stop when cumulative work reaches 1 job.

Step-by-Step Solution:

Verification / Alternative check:Later blocks (if continued) would overshoot; the job is exactly completed at day 50.

Why Other Options Are Wrong:45/54/62/58 days mis-sum block outputs or assume constant crews.

Common Pitfalls:Forgetting that both men and women reduce each cycle; failing to re-compute the rate per block.

Final Answer:50 days