If 4 men can reap a field in 5 days working 12 hours a day, in how many days can 10 men reap the same field working 8 hours a day?

Options

A. 3
B. 2
C. 4
D. 6

Answer

To solve the problem, we need to determine how many days it will take for 10 men to reap the same field while working 8 hours a day, given that 4 men can complete the task in 5 days working 12 hours a day.

### Step-by-Step Solution:

1. **Calculate the Total Work Done by 4 Men:**
- The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Hours per Day} \]
- Here, we have 4 men, working for 5 days, and 12 hours each day:
\[ \text{Total Work} = 4 \text{ men} \times 5 \text{ days} \times 12 \text{ hours/day} = 240 \text{ man-hours} \]

2. **Set Up the Equation for 10 Men Working 8 Hours a Day:**
- Let \( D \) be the number of days required for 10 men to complete the same work. The total work done by 10 men working for \( D \) days at 8 hours a day is:
\[ \text{Total Work} = 10 \text{ men} \times D \text{ days} \times 8 \text{ hours/day} \]
- This can be simplified to:
\[ \text{Total Work} = 80D \text{ man-hours} \]

3. **Equate the Two Expressions for Total Work:**
- Since both expressions represent the same total work, we can set them equal to each other:
\[ 240 = 80D \]

4. **Solve for \( D \):**
- To find \( D \), divide both sides of the equation by 80:
\[ D = \frac{240}{80} = 3 \]

5. **Conclusion:**
- Therefore, it will take 10 men working 8 hours a day a total of **3 days** to reap the same field.

### Final Answer:
**3 days**