If 20 men can reap a field in 38 days, in how many days will 19 men reap the field?

Options

A. 21 days
B. 19 days
C. 76 days
D. 40 days

Answer

To solve the problem of how many days it will take for 19 men to reap a field that 20 men can reap in 38 days, we can follow these steps:

### Step 1: Calculate the total work done in man-days
First, we need to determine the total amount of work required to reap the field in terms of man-days. If 20 men can complete the work in 38 days, we can calculate the total work as follows:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 20 \text{ men} \times 38 \text{ days} = 760 \text{ man-days} \]

### Step 2: Determine the number of days for 19 men to complete the same work
Now, we need to find out how many days it will take for 19 men to complete the same amount of work (760 man-days). We can use the formula:

\[ \text{Number of Days} = \frac{\text{Total Work}}{\text{Number of Men}} = \frac{760 \text{ man-days}}{19 \text{ men}} \]

### Step 3: Perform the division
Now, we calculate the number of days:

\[ \text{Number of Days} = \frac{760}{19} = 40 \text{ days} \]

### Conclusion
Thus, it will take 19 men 40 days to reap the field.

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