If a man completes `3/7` work in 6 days , then how many more days will be require for completing the remaining work ?

Options

A. 8
B. 14
C. 9
D. 7

Answer

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

### Step 1: Understand the total work done
The man completes \( \frac{3}{7} \) of the work in 6 days.

### Step 2: Determine the total work
Let the total work be represented as \( 7x \). This means that \( \frac{3}{7} \) of the total work is \( 3x \).

### Step 3: Calculate the remaining work
The remaining work can be calculated as:
\[ \text{Remaining work} = \text{Total work} - \text{Work done} = 7x - 3x = 4x \]

### Step 4: Find the rate of work
Since the man completes \( 3x \) in 6 days, we can find the rate of work per day:
\[ \text{Rate of work} = \frac{3x}{6} = \frac{x}{2} \text{ (work per day)} \]

### Step 5: Calculate the time required to complete the remaining work
To find out how many days it will take to complete the remaining work \( 4x \):
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Rate of work}} = \frac{4x}{\frac{x}{2}} = 4x \times \frac{2}{x} = 8 \text{ days} \]

### Conclusion
Thus, the man will require **8 more days** to complete the remaining work.

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