10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?

Options

A. `9 h 36 min`
B. 15 h
C. 6 h 40 min
D. 13 h 20 min

Answer

To solve the problem step by step, we can use the concept of work done, which is based on the number of workers and the time taken.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Number of boys (workers) = 10
- Time taken by 10 boys to dig the pitch = 12 hours

2. **Calculate the Total Work Done:**
- Total work can be expressed in terms of "man-hours."
- Work done (W) = Number of boys × Time taken
- So, W = 10 boys × 12 hours = 120 man-hours

3. **Set Up the Equation for 8 Boys:**
- Let the time taken by 8 boys be T hours.
- The work done by 8 boys can also be expressed as:
- Work done = Number of boys × Time taken = 8 boys × T hours

4. **Equate the Total Work Done:**
- Since the total work remains the same, we can set the two expressions for work equal to each other:
- 120 man-hours = 8 boys × T hours

5. **Solve for T:**
- Rearranging the equation gives us:
- T = 120 man-hours / 8 boys
- T = 15 hours

6. **Conclusion:**
- Therefore, 8 boys will take 15 hours to dig the pitch.

### Final Answer:
8 boys will take **15 hours** to dig the pitch.

---