24 men can do a piece of work in 17 days. How many men will be able to do it in 51 days?

Options

A. 8
B. 10
C. 12
D. 6

Explanation

To solve the problem step by step, we can use the concept of work done, which is based on the number of men, the number of days, and the total work.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- We know that 24 men can complete the work in 17 days.

2. **Calculate the Total Work:**
- The total work can be represented in terms of man-days.
- Total work = Number of men × Number of days = 24 men × 17 days = 408 man-days.

3. **Determine the New Scenario:**
- We need to find out how many men (let's denote this as \( m \)) are required to complete the same work in 51 days.

4. **Set Up the Equation:**
- The total work remains the same, so we can set up the equation:
\[ m \times 51 \text{ days} = 408 \text{ man-days} \]

5. **Solve for \( m \):**
- Rearranging the equation gives:
\[ m = \frac{408}{51} \]
- Now, perform the division:
\[ m = 8 \]

6. **Conclusion:**
- Therefore, 8 men will be able to complete the work in 51 days.

### Final Answer:
8 men.

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