15 men can complete a piece of work in 32 days. How many men can complete the work in 12 days ?

Options

A. 40
B. 42
C. 38
D. 32

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total work done
We know that 15 men can complete the work in 32 days. To find the total work, we can use the formula:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]

Substituting the values:

\[ \text{Total Work} = 15 \text{ men} \times 32 \text{ days} = 480 \text{ man-days} \]

### Step 2: Determine the number of men required to complete the work in 12 days
Now, we want to find out how many men are needed to complete the same amount of work (480 man-days) in 12 days. We can set up the equation:

\[ \text{Number of Men} = \frac{\text{Total Work}}{\text{Number of Days}} \]

Substituting the values:

\[ \text{Number of Men} = \frac{480 \text{ man-days}}{12 \text{ days}} = 40 \text{ men} \]

### Conclusion
Thus, the number of men required to complete the work in 12 days is **40 men**.

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