3 men dig a hole in 10 days. How many days would it take for 5 men to dig the same hole?

Options

A. `(50)/(3)`
B. 7
C. 5
D. 6

Answer

To solve the problem of how many days it would take for 5 men to dig the same hole that 3 men can dig in 10 days, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Work Done**:
- We know that 3 men can dig a hole in 10 days.
- To find the total work in terms of "man-days", we multiply the number of men by the number of days:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 3 \text{ men} \times 10 \text{ days} = 30 \text{ man-days} \]

2. **Set Up the Equation for 5 Men**:
- Let \( x \) be the number of days it takes for 5 men to dig the same hole.
- The total work done by 5 men in \( x \) days can also be expressed in man-days:
\[ \text{Total Work} = 5 \text{ men} \times x \text{ days} = 5x \text{ man-days} \]

3. **Equate the Total Work**:
- Since both expressions represent the same total work, we can set them equal to each other:
\[ 5x = 30 \]

4. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 5:
\[ x = \frac{30}{5} = 6 \]

5. **Conclusion**:
- Therefore, it would take 5 men 6 days to dig the same hole.

### Final Answer:
The answer is **6 days**.