If 10 men can reap a field in 57 days, In how many days will 19 men reap the field?

Options

A. 21 days
B. 19 days
C. 76 days
D. 30 days

Answer

To solve the problem of how many days it will take for 19 men to reap a field that 10 men can reap in 57 days, we can use the concept of work done, which is defined as the product of the number of men and the number of days they work.

### Step-by-Step Solution:

1. **Calculate Total Work Done by 10 Men**:
- Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
- Here, the number of men is 10 and the number of days is 57.
\[ \text{Total Work} = 10 \times 57 = 570 \text{ units} \]

2. **Set Up the Equation for 19 Men**:
- Let \( x \) be the number of days it takes for 19 men to reap the same field.
- The total work done by 19 men can be expressed as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
- So, for 19 men, the equation becomes:
\[ 19 \times x = 570 \]

3. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 19:
\[ x = \frac{570}{19} \]

4. **Calculate \( x \)**:
- Performing the division:
\[ x = 30 \]

5. **Conclusion**:
- Therefore, it will take 19 men 30 days to reap the field.

### Final Answer:
19 men will reap the field in **30 days**.