45 men can complete a piece of work in 12 days. In how many days will 36 men be able to complete it?

Options

A. 10
B. 16
C. 18
D. 15

Answer

To solve the problem, we will use the concept of man-days, which states that the total amount of work done is equal to the number of men multiplied by the number of days they work.

### Step-by-step Solution:

1. **Identify the given information:**
- Number of men (m1) = 45
- Number of days (d1) = 12
- Number of men (m2) = 36
- Number of days (d2) = ?

2. **Calculate the total work in man-days:**
- Total work = Number of men × Number of days
- Total work = m1 × d1 = 45 men × 12 days = 540 man-days

3. **Set up the equation for the second scenario:**
- Total work = m2 × d2
- Therefore, 540 man-days = 36 men × d2

4. **Solve for d2:**
- Rearranging the equation gives us:
\[ d2 = \frac{540 \text{ man-days}}{36 \text{ men}} \]
- Now, perform the division:
\[ d2 = 15 \text{ days} \]

5. **Conclusion:**
- Therefore, 36 men will be able to complete the work in **15 days**.

### Final Answer:
The answer is **15 days** (Option D).

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