If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be

Options

A. 12 days
B. 10 days
C. 9 days
D. 8 days

Answer

To solve the problem of how long it will take for 12 men to complete the same piece of work that 10 men can do in 12 days, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- 10 men can complete the work in 12 days.

2. **Calculate the Total Work**:
- The total work can be expressed in terms of man-days.
- Total work = Number of men × Number of days = 10 men × 12 days = 120 man-days.

3. **Set Up the Equation for 12 Men**:
- Let the number of days taken by 12 men to complete the same work be \( d \).
- The total work done by 12 men in \( d \) days can also be expressed as:
- Total work = Number of men × Number of days = 12 men × \( d \) days = 12d man-days.

4. **Equate the Two Expressions for Total Work**:
- Since the total work is the same, we can set the two expressions equal to each other:
\[ 120 = 12d \]

5. **Solve for \( d \)**:
- To find \( d \), divide both sides of the equation by 12:
\[ d = \frac{120}{12} = 10 \]

6. **Conclusion**:
- Therefore, the time taken by 12 men to complete the same piece of work is **10 days**.

### Final Answer:
The time taken by 12 men to do the same piece of work will be **10 days**.