If 36 men can complete a piece of work in 25 hours of continuous work, then in how many hours will 15 men complete the same work, assuming all men work at the same constant rate?

Introduction / Context:
This question is a straightforward application of the inverse proportionality between number of workers and time taken when the total work is fixed. It checks whether you can calculate total man-hours and then adjust the time when the workforce changes.

Given Data / Assumptions:
- 36 men can complete the work in 25 hours.
- We need the time required if only 15 men are working.
- Total work remains the same in both cases.
- All men work at identical and constant efficiency.

Concept / Approach:
Total work can be measured in man-hours. If the work requires a certain number of man-hours, then:
- Work W = men * hours.
First, we compute the man-hours needed using the initial data (36 men, 25 hours). Then we divide that same number of man-hours by the new number of men (15 men) to get the new time.

Step-by-Step Solution:
Step 1: Calculate the total man-hours required using the first situation: W = 36 * 25.Step 2: Compute: 36 * 25 = 900 man-hours.Step 3: For 15 men, let the required time be T hours.Step 4: Then 15 * T = 900 man-hours (since total work is unchanged).Step 5: Solve for T: T = 900 / 15.Step 6: T = 60 hours.

Verification / Alternative check:
The time is inversely proportional to the number of men when total work is fixed. So, T2 / T1 = M1 / M2 = 36 / 15 = 12 / 5 = 2.4. Since the original time T1 is 25 hours, T2 = 25 * 2.4 = 60 hours. This matches our earlier calculation.

Why Other Options Are Wrong:
Values like 40 or 50 hours are too small and would imply that fewer men somehow finish the work faster, which contradicts the inverse relationship. 70 hours is larger than necessary and would represent more than the required man-hours. Only 60 hours preserves the original total of 900 man-hours.

Common Pitfalls:
Students might mistakenly assume a direct proportion (more men, more time) instead of the correct inverse proportion, or they may forget to hold total work constant. Miscalculations like 36 * 25 or dividing 900 incorrectly are also common. Always compute total man-hours first and then divide by the new workforce to stay consistent.

Final Answer:
15 men will complete the work in 60 hours.