Prashnath is twice as good a sportsman as Tarun and together they finish a piece of work in 21 days. In how many days with Rarun alone finish the work ?
A. 42
B. 63
C. 84
D. 50

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem, we need to determine how many days Tarun alone would take to finish the work, given that Prashanth is twice as efficient as Tarun and together they can complete the work in 21 days.

### Step-by-Step Solution:

1. **Define the Efficiencies**:
- Let Tarun's efficiency be \( x \).
- Since Prashanth is twice as good as Tarun, Prashanth's efficiency will be \( 2x \).

2. **Calculate Combined Efficiency**:
- The combined efficiency of Prashanth and Tarun is:
\[ \text{Combined Efficiency} = x + 2x = 3x \]

3. **Determine Total Work Done**:
- They complete the work together in 21 days. Therefore, the total work can be calculated as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Days} = 3x \times 21 = 63x \]

4. **Calculate Time Taken by Tarun Alone**:
- To find out how many days Tarun would take to finish the work alone, we use his efficiency:
\[ \text{Days taken by Tarun} = \frac{\text{Total Work}}{\text{Tarun's Efficiency}} = \frac{63x}{x} = 63 \text{ days} \]

Thus, Tarun alone can finish the work in **63 days**.

### Final Answer:
**Option B: 63**