56 workers can reap a field in 8 days. If the work is to be completed in 7 days, the extra workers needed are:

Options

A. 7
B. 8
C. 14
D. 16

Answer

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

### Step 1: Determine the total work done in worker-days
The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Workers} \times \text{Number of Days} \]
Given that 56 workers can reap a field in 8 days, we calculate:
\[ \text{Total Work} = 56 \text{ workers} \times 8 \text{ days} = 448 \text{ worker-days} \]

### Step 2: Calculate the number of workers needed to complete the work in 7 days
If the work needs to be completed in 7 days, we can find out how many workers are needed by rearranging the total work formula:
\[ \text{Number of Workers} = \frac{\text{Total Work}}{\text{Number of Days}} \]
Substituting the values we have:
\[ \text{Number of Workers} = \frac{448 \text{ worker-days}}{7 \text{ days}} = 64 \text{ workers} \]

### Step 3: Calculate the extra workers needed
Now, we need to find out how many extra workers are required. We already have 56 workers, so:
\[ \text{Extra Workers Needed} = \text{Workers Required} - \text{Current Workers} \]
Substituting the values:
\[ \text{Extra Workers Needed} = 64 \text{ workers} - 56 \text{ workers} = 8 \text{ workers} \]

### Final Answer
The extra workers needed are **8 workers**.

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