Equivalent work (man-hour balancing): 20 workers working 5 hours per day finish a job in 10 days. If instead 25 workers are employed for 10 hours per day, how many days will be required to complete the same job?

Introduction / Context:With uniform productivity, total work is proportional to (workers × hours/day × days). Balance man-hours between the two scenarios to find the unknown days.

Given Data / Assumptions:

• Scenario 1: 20 workers × 5 h/day × 10 days.
• Scenario 2: 25 workers × 10 h/day × D days.

Concept / Approach:Set total man-hours equal between the two scenarios.

Step-by-Step Solution:Total (1) = 20 * 5 * 10 = 1000 man-hours.Let D be required days in scenario (2): 25 * 10 * D = 1000 ⇒ 250D = 1000 ⇒ D = 4.

Verification / Alternative check:Intuitively, scenario (2) has 2.5 times the daily man-hours (25 * 10 vs 20 * 5 = 250 vs 100), hence time shrinks by 1000/250 = 4 days.

Why Other Options Are Wrong:3, 5, 6, 8 days do not preserve equality of total man-hours for the same job.

Common Pitfalls:Comparing only workers or only hours per day without multiplying both.

Final Answer:4 days