If 60 boys can finish a work in 15 days by working 8 hours a day, then how many hours a day should 72 boys work to finish that work within 20 days?

Options

A. 4
B. 6
C. 5
D. 7

Answer

To solve the problem, we will use the concept of "man-days," which is a way to quantify the amount of work done based on the number of workers, the number of days they work, and the hours they work each day.

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of boys (workers) in the first scenario, \( m_1 = 60 \)
- Number of days in the first scenario, \( d_1 = 15 \)
- Number of hours worked per day in the first scenario, \( h_1 = 8 \)
- Number of boys in the second scenario, \( m_2 = 72 \)
- Number of days in the second scenario, \( d_2 = 20 \)
- Number of hours worked per day in the second scenario, \( h_2 = ? \) (this is what we need to find)

2. **Set up the equation using the man-days formula:**
\[ m_1 \times d_1 \times h_1 = m_2 \times d_2 \times h_2 \]
Substituting the known values:
\[ 60 \times 15 \times 8 = 72 \times 20 \times h_2 \]

3. **Calculate the left side of the equation:**
\[ 60 \times 15 = 900 \]
\[ 900 \times 8 = 7200 \]
So, the left side becomes:
\[ 7200 = 72 \times 20 \times h_2 \]

4. **Calculate the right side without \( h_2 \):**
\[ 72 \times 20 = 1440 \]
Thus, we have:
\[ 7200 = 1440 \times h_2 \]

5. **Solve for \( h_2 \):**
\[ h_2 = \frac{7200}{1440} \]
\[ h_2 = 5 \]

6. **Conclusion:**
The number of hours per day that 72 boys should work to finish the work in 20 days is \( 5 \) hours.

### Final Answer:
**5 hours a day**