If 25 men can do a work in 36 days, in how many days will 15 men do it?

Question

Accepted Answer

To determine how many days 15 men will take to complete the same work that 25 men can do in 36 days, we can use the concept of man-days, which is a measure of the total amount of work done.

1. **Calculate the total amount of work in man-days:**
   - If 25 men can complete the work in 36 days, the total work is $25 \times 36 = 900$ man-days.

2. **Determine how many days 15 men will take to complete the same amount of work:**
   - We need to find the number of days ($d$) such that 15 men working for $d$ days will complete 900 man-days of work.
   - The equation is $15 \times d = 900$.
   - Solving for $d$, we get $d = \frac{900}{15} = 60$.

Therefore, 15 men will take 60 days to complete the work. This supports Option 4 as the correct answer.

**Explanation of why other options are incorrect:**

- **Option 1 (40 days):** If 15 men were to complete the work in 40 days, the total man-days would be $15 \times 40 = 600$ man-days, which is less than the required 900 man-days. Hence, this option is incorrect.

- **Option 2 (50 days):** If 15 men were to complete the work in 50 days, the total man-days would be $15 \times 50 = 750$ man-days, which is still less than the required 900 man-days. Therefore, this option is incorrect.

- **Option 3 (52 days):** If 15 men were to complete the work in 52 days, the total man-days would be $15 \times 52 = 780$ man-days, which is also less than the required 900 man-days. Thus, this option is incorrect.

In conclusion, Option 4 (60 days) is the only correct answer, as it accurately reflects the number of days 15 men would need to complete the work, based on the total man-days calculation.