A canal of a village can be cleaned by 24 villagers in 12 days. The number of days in which 36 villagers can clean the canal is?

Options

A. 1. 18
B. 2. 8
C. 3. 72
D. 4. 16

Answer

To solve the problem, we can use the concept of man-days, which states that the total work done is equal to the number of workers multiplied by the number of days they work.

### Step-by-step Solution:

1. **Understand the given data**:
- Number of villagers (M1) = 24
- Number of days (D1) = 12
- Number of villagers in the second case (M2) = 36
- Number of days in the second case (D2) = ?

2. **Calculate total work done in the first case**:
- Total work can be calculated as:
\[ \text{Total Work} = M1 \times D1 = 24 \text{ villagers} \times 12 \text{ days} = 288 \text{ villager-days} \]

3. **Set up the equation for the second case**:
- In the second case, the total work done should be the same:
\[ \text{Total Work} = M2 \times D2 = 36 \text{ villagers} \times D2 \]

4. **Equate the total work from both cases**:
- Since the total work is the same, we can set up the equation:
\[ 288 = 36 \times D2 \]

5. **Solve for D2**:
- To find D2, divide both sides of the equation by 36:
\[ D2 = \frac{288}{36} = 8 \text{ days} \]

### Conclusion:
The number of days in which 36 villagers can clean the canal is **8 days**.

---