If 15 men can complete a piece of work in 30 days, in how many days will 18 men complete it ?

Answer

To solve the problem step by step, we can use the concept of direct variation. The number of men and the number of days taken to complete the work are inversely proportional. This means that as the number of men increases, the number of days taken decreases.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- 15 men can complete the work in 30 days.

2. **Calculate the Total Work in Man-Days**:
- Total work can be calculated as the product of the number of men and the number of days they work.
- Total work = Number of men × Number of days = 15 men × 30 days = 450 man-days.

3. **Determine the Work Done by One Man**:
- Since 15 men take 30 days to complete the work, we can find out how many days one man would take to complete the same work alone.
- One man would take 450 days to complete the work (since he would have to do the work of all 15 men).

4. **Calculate the Time Taken by 18 Men**:
- Now, if we have 18 men working, we can find out how many days they would take to complete the same amount of work.
- Since the work is constant, we can use the formula:
\[ \text{Days taken by 18 men} = \frac{\text{Total work in man-days}}{\text{Number of men}} = \frac{450 \text{ man-days}}{18 \text{ men}}. \]
- Performing the calculation:
\[ \frac{450}{18} = 25 \text{ days}. \]

5. **Conclusion**:
- Therefore, 18 men will complete the work in 25 days.

### Final Answer:
18 men will complete the work in **25 days**.

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