Man-days method: If 15 men complete a work in 16 days, in how many days will 24 men complete the same work (assume identical efficiency for all men)?

Introduction / Context:
This question uses conservation of man-days (work = workers * days) under the assumption that all workers are equally efficient. Increasing the number of workers should reduce the time proportionally for the same total amount of work.

Given Data / Assumptions:

• 15 men finish the job in 16 days.
• All men have equal efficiency; work scale is linear.
• We need time for 24 men to do the same job.

Concept / Approach:
Compute the total man-days from the first scenario, then divide by the new workforce to get the required time. Formula: days_2 = (men_1 * days_1) / men_2.

Step-by-Step Solution:
Total man-days = 15 * 16 = 240. With 24 men, required days = 240 / 24 = 10.

Verification / Alternative check:
Ratio method: Time varies inversely with men. 24/15 = 8/5 ⇒ time factor = 5/8 ⇒ 16 * 5/8 = 10 days.

Why Other Options Are Wrong:
7, 8, or 12 days do not match the linear inverse proportion implied by identical efficiencies.

Common Pitfalls:
Forgetting that the product men * days remains constant for the same total work when efficiency is unchanged.

Final Answer:
10 days