16 workers working 8 hours per day can demolish a building in 32 days. In how many days 24 workers working 12 hours per day can demolish the same building?

Options

A. `frac 128 3` days
B. `frac 56 3` days
C. `frac128 9` days
D. `frac56 9` days

Answer

To solve the problem, we can use the concept of work done, which can be expressed in terms of the number of workers, the number of days they work, and the number of hours they work each day. The relationship can be summarized with the formula:

\[ M \times D \times H = W \]

Where:
- \( M \) = Number of workers
- \( D \) = Number of days
- \( H \) = Number of hours worked per day
- \( W \) = Total work done (which we can consider as 1 for this problem since we are looking for the same building to be demolished)

### Step-by-Step Solution:

1. **Calculate the total work done by the first group of workers:**
- Number of workers (M1) = 16
- Hours per day (H1) = 8
- Days (D1) = 32

Using the formula:
\[ W = M1 \times D1 \times H1 = 16 \times 32 \times 8 \]

2. **Calculate the total work done:**
\[ W = 16 \times 32 \times 8 = 4096 \text{ worker-hours} \]

3. **Set up the equation for the second group of workers:**
- Number of workers (M2) = 24
- Hours per day (H2) = 12
- Days (D2) = ?

Using the same formula:
\[ W = M2 \times D2 \times H2 \]
Substituting the known values:
\[ 4096 = 24 \times D2 \times 12 \]

4. **Solve for D2:**
\[ 4096 = 288 \times D2 \]
\[ D2 = \frac{4096}{288} \]

5. **Calculate D2:**
\[ D2 = \frac{4096 \div 16}{288 \div 16} = \frac{256}{18} = \frac{128}{9} \]

### Conclusion:
Thus, the number of days required for 24 workers working 12 hours per day to demolish the same building is \( \frac{128}{9} \) days.