If 36 men can complete a piece of work in 25 hours, in how many hours will 15 men complete the same work, assuming the work rate is uniform?

Introduction / Context:
This question is a time and work problem based on inverse proportionality between number of workers and time taken, when total work is fixed and each worker has a constant rate. Such problems commonly appear in aptitude tests to test understanding of how changing the number of workers affects the completion time for the same task.

Given Data / Assumptions:

• Thirty six men can complete the work in 25 hours.
• We need to find how many hours 15 men will take to complete the same work.
• All men work at the same constant rate.
• The total amount of work remains unchanged between the two situations.

Concept / Approach:
When work is fixed, the relationship between number of workers and time is inversely proportional. That means men * time is constant for a fixed task if work rate per man does not change. Thus, we can relate the two situations by equating the products of men and time. Solving this equation gives the required time for the second group of men.

Step-by-Step Solution:
Step 1: Let T be the number of hours for which 15 men must work to complete the job.Step 2: In the first case, the total man hours are 36 * 25.Step 3: In the second case, the total man hours are 15 * T.Step 4: Since total work is the same, set the products equal: 36 * 25 = 15 * T.Step 5: Compute 36 * 25 = 900. Then T = 900 / 15 = 60 hours.
Verification / Alternative check:
We can check proportionality. If the number of men is reduced from 36 to 18, halving the workforce, time should double from 25 to 50 hours. Reducing further from 18 to 9 should again double the time to 100 hours. Since 15 lies between 18 and 9, a time of 60 hours is reasonable and fits the exact algebraic result. A direct calculation of man hours confirms that 36 men for 25 hours and 15 men for 60 hours both contribute 900 man hours, which must correspond to the same total work.

Why Other Options Are Wrong:
Forty hours would give 15 * 40 = 600 man hours, which is less than the required 900, so the work would remain incomplete.Fifty hours would produce 15 * 50 = 750 man hours, still short of the needed 900.Seventy hours would give 15 * 70 = 1050 man hours, which exceeds the total work and implies extra unused capacity.
Common Pitfalls:
Some candidates incorrectly treat the relationship as directly proportional and set up equations like 36 / 15 = 25 / T, which reverses the logic. Others forget to check dimensions and end up with non sensible results. Writing the relationship clearly as men1 * time1 = men2 * time2 for the same work is the easiest way to avoid these errors and quickly arrive at the correct answer.

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