Ehsaan is twice as good a worker as Kamal and together they finish a piece of work in 29 days. In how many days will Kamal, working alone, finish the work?

Options

A. 58
B. 70
C. 87
D. 116

Answer

To solve the problem, we need to find out how many days Kamal will take to finish the work alone, given that Ehsaan is twice as efficient as Kamal and they complete the work together in 29 days.

### Step-by-Step Solution:

1. **Define the efficiencies**:
- Let Kamal's efficiency be \( K \) (amount of work done by Kamal in one day).
- Since Ehsaan is twice as good a worker as Kamal, Ehsaan's efficiency will be \( 2K \).

2. **Combined efficiency**:
- When both work together, their combined efficiency is:
\[ K + 2K = 3K \]

3. **Total work done**:
- If they complete the work together in 29 days, the total work can be expressed as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} = 3K \times 29 \]
- Therefore, the total work is \( 87K \).

4. **Kamal's time to finish the work alone**:
- The time taken by Kamal to finish the same total work alone can be calculated as:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Kamal's Efficiency}} = \frac{87K}{K} = 87 \text{ days} \]

Thus, Kamal will finish the work alone in **87 days**.