If 30men working 18h per day can reap a field in 32 days, in how many days can 36 men reap the field working 16h per day ?

Answer

To solve the problem step by step, we will use the concept of the Unitary Method and the relationship between the number of men, the number of days, and the number of hours worked.

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of men in the first scenario (X1) = 30 men
- Number of hours worked per day in the first scenario (Z1) = 18 hours
- Number of days taken to reap the field in the first scenario (Y1) = 32 days

- Number of men in the second scenario (X2) = 36 men
- Number of hours worked per day in the second scenario (Z2) = 16 hours
- Number of days taken to reap the field in the second scenario (Y2) = ? (This is what we need to find)

2. **Set up the relationship using the formula:**
The work done can be expressed as:
\[ X1 \times Y1 \times Z1 = X2 \times Y2 \times Z2 \]
Substituting the known values:
\[ 30 \times 32 \times 18 = 36 \times Y2 \times 16 \]

3. **Calculate the left side of the equation:**
\[ 30 \times 32 \times 18 = 17280 \]
So, we have:
\[ 17280 = 36 \times Y2 \times 16 \]

4. **Simplify the right side:**
\[ 36 \times 16 = 576 \]
Now, the equation becomes:
\[ 17280 = 576 \times Y2 \]

5. **Solve for Y2:**
\[ Y2 = \frac{17280}{576} \]

6. **Calculate Y2:**
\[ Y2 = 30 \]

### Final Answer:
Thus, 36 men working 16 hours per day can reap the field in **30 days**.