12 men can reap a field in 25 days. In how many days can 20 men reap the same field?

Options

A. 65 days
B. 35 days
C. 15 days
D. 25 days

Answer

To solve the problem of how many days 20 men can reap the same field that 12 men can reap in 25 days, we can follow these steps:

### Step 1: Calculate the total work done in man-days
First, we need to find out the total amount of work done in man-days by the 12 men over 25 days.

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} \]
\[ \text{Total work} = 12 \text{ men} \times 25 \text{ days} = 300 \text{ man-days} \]

### Step 2: Determine how many days it takes for 20 men to complete the same work
Now, we need to find out how many days (let's call it \( x \)) it will take for 20 men to complete the same amount of work (300 man-days).

Using the formula for total work again, we have:

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} \]
\[ 300 \text{ man-days} = 20 \text{ men} \times x \text{ days} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:

\[ x = \frac{300 \text{ man-days}}{20 \text{ men}} = 15 \text{ days} \]

### Conclusion
Thus, 20 men can reap the same field in **15 days**.

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