Equivalent man-hours across scenarios: 39 persons repair a road in 12 days at 5 h/day. In how many days will 30 persons at 6 h/day complete the same work?

Introduction / Context:
The quantity of work is proportional to total man-hours = persons * hours/day * days. If the work is the same, equate the man-hours of the two scenarios and solve for the unknown number of days in the second scenario. This is a direct application of the unitary method for work-rate problems.

Given Data / Assumptions:

• Scenario A: 39 persons, 12 days, 5 h/day
• Scenario B: 30 persons, D days, 6 h/day
• Same work; constant efficiency

Concept / Approach:
Man-hours A = Man-hours B ⇒ 39*12*5 = 30*D*6. Solve for D algebraically. Avoid canceling prematurely to prevent arithmetic slips.

Step-by-Step Solution:

Verification / Alternative check:
Back-check: 30*6*13 = 2340 man-hours, which equals the original requirement, so the same work is completed.

Why Other Options Are Wrong:

• 9, 12, 14, 10: These values do not balance man-hours to 2340 under 30 workers at 6 h/day.

Common Pitfalls:
Confusing proportionality (fewer workers at more hours) or dropping a factor of hours/day. Always compute total man-hours explicitly.

Final Answer:
13