16 persons can reap 1/5th field in 6 days. How many persons (with same efficiency) are required to reap rest of the field in 8 days?

Options

A. 27
B. 54
C. 48
D. 64

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the total work done by 16 persons in 6 days
Given that 16 persons can reap 1/5 of the field in 6 days, we can calculate the total work done in terms of "man-days."

Total work done by 16 persons in 6 days:
\[ \text{Work} = \text{Number of persons} \times \text{Number of days} = 16 \text{ persons} \times 6 \text{ days} = 96 \text{ man-days} \]
This means that 96 man-days are required to reap 1/5 of the field.

### Step 2: Calculate the total work required for the entire field
Since 1/5 of the field requires 96 man-days, the total work required for the entire field (5/5) can be calculated as follows:
\[ \text{Total Work} = 96 \text{ man-days} \times 5 = 480 \text{ man-days} \]

### Step 3: Determine the remaining work to be done
Since 1/5 of the field has already been completed, the remaining work is:
\[ \text{Remaining Work} = 480 \text{ man-days} - 96 \text{ man-days} = 384 \text{ man-days} \]

### Step 4: Calculate the number of persons required to complete the remaining work in 8 days
Let \( m \) be the number of persons required to complete the remaining 384 man-days of work in 8 days. We can set up the equation:
\[ m \text{ persons} \times 8 \text{ days} = 384 \text{ man-days} \]
Solving for \( m \):
\[ m = \frac{384 \text{ man-days}}{8 \text{ days}} = 48 \text{ persons} \]

### Final Answer
Thus, the number of persons required to reap the rest of the field in 8 days is **48 persons**.

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