If 5 men working 6 hours a day can reap a field in 20 days. In how many days will 15 men reap the field, working 8 hours a day ?

Options

A. 5 days
B. 6 days
C. 7 1/2 days
D. 9 days

Answer

To solve the problem, we will use the concept of work done, which is calculated as the product of the number of workers, the number of hours they work per day, and the number of days they work.

### Step-by-Step Solution:

1. **Calculate the total work done in man-hours:**
- Given that 5 men can reap the field in 20 days working 6 hours a day, we can calculate the total work done.
- Total work = Number of men × Number of hours per day × Number of days
- Total work = 5 men × 6 hours/day × 20 days
- Total work = 600 man-hours

2. **Determine the work rate of the new group:**
- Now we need to find out how many days it will take for 15 men working 8 hours a day to complete the same amount of work (600 man-hours).
- Let the number of days required be \( d \).
- Total work done by 15 men in \( d \) days = 15 men × 8 hours/day × \( d \) days
- Total work = 120d man-hours

3. **Set up the equation:**
- Since both scenarios represent the same amount of work, we can set the equations equal to each other:
- 120d = 600

4. **Solve for \( d \):**
- To find \( d \), divide both sides by 120:
- \( d = \frac{600}{120} \)
- \( d = 5 \)

5. **Conclusion:**
- Therefore, it will take 15 men working 8 hours a day a total of 5 days to reap the field.

### Final Answer:
The number of days required for 15 men working 8 hours a day to reap the field is **5 days**.

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