42 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. 6
C. 14
D. 16

Answer

To solve the problem step by step, we will calculate the total work done, determine how many workers are needed to complete the work in the desired time, and then find out how many extra workers are required.

### Step 1: Calculate the Total Work
The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Workers} \times \text{Number of Days} \]

Given:
- Number of Workers = 42
- Number of Days = 8

Now, substituting the values:
\[ \text{Total Work} = 42 \times 8 = 336 \text{ units} \]

### Step 2: Determine the Number of Workers Needed for 7 Days
Now, we need to find out how many workers are required to complete the same amount of work (336 units) in 7 days. We can rearrange the formula:
\[ \text{Number of Workers} = \frac{\text{Total Work}}{\text{Number of Days}} \]

Substituting the values:
\[ \text{Number of Workers} = \frac{336}{7} = 48 \text{ workers} \]

### Step 3: Calculate the Extra Workers Needed
To find the extra workers needed, we subtract the original number of workers from the number of workers required to complete the work in 7 days:
\[ \text{Extra Workers} = \text{Workers Needed} - \text{Original Workers} \]

Substituting the values:
\[ \text{Extra Workers} = 48 - 42 = 6 \text{ extra workers} \]

### Conclusion
Therefore, the number of extra workers needed to complete the work in 7 days is **6**.

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