If 35 men can reap a field in 8 days, in how many days can 20 men reap the same field?

Answer

To solve the problem of how many days it will take for 20 men to reap the same field that 35 men can reap in 8 days, we can use the concept of inverse proportions.

### Step-by-Step Solution:

1. **Identify the relationship**: We know that if the number of men decreases, the number of days required to complete the work will increase. This is an example of inverse proportion.

2. **Set up the proportion**: We can set up the relationship based on the given data:
- Let \( M_1 = 35 \) (the number of men)
- Let \( D_1 = 8 \) (the number of days taken by 35 men)
- Let \( M_2 = 20 \) (the number of men we want to find the days for)
- Let \( D_2 \) be the number of days taken by 20 men.

According to the inverse proportion, we have:
\[ M_1 \times D_1 = M_2 \times D_2 \]
Substituting the known values:
\[ 35 \times 8 = 20 \times D_2 \]

3. **Calculate the left side**: First, calculate \( 35 \times 8 \):
\[ 35 \times 8 = 280 \]

4. **Set up the equation**: Now we have:
\[ 280 = 20 \times D_2 \]

5. **Solve for \( D_2 \)**: To find \( D_2 \), divide both sides by 20:
\[ D_2 = \frac{280}{20} \]

6. **Calculate \( D_2 \)**: Now perform the division:
\[ D_2 = 14 \]

### Conclusion:
Therefore, it will take 20 men **14 days** to reap the same field.

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