If 30 men working 9 h per day can reap a field in 16 days, in how many days, will 36 men reap the field working 8 h per day ?

Options

A. 15
B. 25
C. 18
D. 10

Answer

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

### Step 1: Understand the given information
We know that:
- 30 men work for 9 hours a day for 16 days to reap the field.

### Step 2: Calculate the total work done in man-hours
Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
For the first scenario:
\[ \text{Total Work} = 30 \text{ men} \times 9 \text{ hours/day} \times 16 \text{ days} \]
Calculating this:
\[ \text{Total Work} = 30 \times 9 \times 16 = 4320 \text{ man-hours} \]

### Step 3: Set up the equation for the second scenario
Now, we need to find out how many days (let's call it \( z_2 \)) it will take for 36 men working 8 hours a day to reap the same field. The total work remains the same (4320 man-hours).

Using the formula for total work again:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
For the second scenario:
\[ 4320 = 36 \text{ men} \times 8 \text{ hours/day} \times z_2 \]

### Step 4: Solve for \( z_2 \)
Rearranging the equation to solve for \( z_2 \):
\[ z_2 = \frac{4320}{36 \times 8} \]
Calculating the denominator:
\[ 36 \times 8 = 288 \]
Now substituting back:
\[ z_2 = \frac{4320}{288} \]
Calculating \( z_2 \):
\[ z_2 = 15 \text{ days} \]

### Conclusion
Thus, 36 men working 8 hours a day will reap the field in **15 days**.

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