Thirty men working 9 hours per day can reap a field in 16 days. If 36 men work 8 hours per day at the same efficiency, in how many days will they reap the field?

Introduction:
When both workforce size and daily hours change, total work is proportional to men × hours/day × days. By equating total man-hours between the two scenarios for the same task, we can solve for the unknown number of days directly and cleanly.

Given Data / Assumptions:

• Scenario 1 (baseline): 30 men, 9 h/day, 16 days.
• Scenario 2: 36 men, 8 h/day, D days.
• Efficiency per man-hour remains constant.

Concept / Approach:
Total man-hours are equal: 30 * 9 * 16 = 36 * 8 * D. Solve for D using simple algebra and integer arithmetic where possible to avoid rounding errors.

Step-by-Step Solution:

Verification / Alternative check:
Ratio method: D = 16 * (30/36) * (9/8) = 16 * (5/6) * (9/8) = 16 * (45/48) = 15, confirming the result.

Why Other Options Are Wrong:
25, 18, 12, 10 fail the equality of total man-hours for the unchanged job scope.

Common Pitfalls:
Treating men and hours symmetrically but forgetting to multiply both before applying inverse proportion in days; always equate the product men * hours/day * days.

Final Answer:
15