14 men complete a work in 18 days. If 21 men are employed, then the time required to complete the same work will be:

Options

A. 14 days
B. 10 days
C. 15 days
D. 12 days

Answer

To solve the problem step by step, we can use the concept of man-days, which is the product of the number of men and the number of days they work.

### Step-by-Step Solution:

1. **Identify the given data:**
- Number of men (M1) = 14
- Time taken by these men (T1) = 18 days
- Number of men employed later (M2) = 21
- Time taken by these men (T2) = ?

2. **Calculate total work in man-days:**
- Total work = M1 × T1
- Total work = 14 men × 18 days = 252 man-days

3. **Set up the equation for the second scenario:**
- We know that the total work remains the same, so:
- Total work = M2 × T2
- 252 man-days = 21 men × T2

4. **Solve for T2:**
- Rearranging the equation gives us:
- T2 = Total work / M2
- T2 = 252 man-days / 21 men

5. **Perform the division:**
- T2 = 12 days

### Conclusion:
The time required to complete the same work with 21 men is **12 days**.