If 12 men can finish a work in 20 days , then find the number of days required to complete the same work by15 men .

Answer

To solve the problem of how many days 15 men will take to complete the same work that 12 men can finish in 20 days, we can follow these steps:

### Step 1: Calculate the total work done in man-days
First, we need to determine the total work in terms of man-days. If 12 men can finish the work in 20 days, we can calculate the total work as follows:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 12 \text{ men} \times 20 \text{ days} = 240 \text{ man-days} \]

### Step 2: Determine the work rate of 15 men
Next, we need to find out how many days it will take for 15 men to complete the same total work of 240 man-days. Let \( x \) be the number of days required for 15 men to finish the work. The equation can be set up as follows:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
\[ 240 \text{ man-days} = 15 \text{ men} \times x \text{ days} \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{240 \text{ man-days}}{15 \text{ men}} = 16 \text{ days} \]

### Conclusion
Thus, 15 men will take **16 days** to complete the same work.

---