Atul and Binay together complete a piece of work in 5 days. If Binay alone can complete the same work in 8 days, how many days can Atul take to complete the same work alone?
A. 40/3 days
B. 20/3 days
C. 9 days
D. 10 days

Options

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

Answer

To solve the problem step by step, we need to find out how many days Atul alone can complete the work.

### Step-by-Step Solution:

1. **Understanding the Work Rates**:
- Atul and Binay together complete the work in 5 days.
- Binay alone can complete the work in 8 days.

2. **Finding Work Done by Binay**:
- If Binay can complete the work in 8 days, his work rate is:
\[ \text{Work rate of Binay} = \frac{1 \text{ work}}{8 \text{ days}} = \frac{1}{8} \text{ work per day} \]

3. **Finding Work Done by Atul and Binay Together**:
- If Atul and Binay together complete the work in 5 days, their combined work rate is:
\[ \text{Combined work rate} = \frac{1 \text{ work}}{5 \text{ days}} = \frac{1}{5} \text{ work per day} \]

4. **Finding Work Done by Atul Alone**:
- Let Atul's work rate be \( A \). We know that:
\[ A + \text{Work rate of Binay} = \text{Combined work rate} \]
- Substituting the known values:
\[ A + \frac{1}{8} = \frac{1}{5} \]

5. **Solving for Atul's Work Rate**:
- To solve for \( A \), we first need a common denominator for \( \frac{1}{5} \) and \( \frac{1}{8} \). The least common multiple of 5 and 8 is 40.
- Rewrite the fractions:
\[ A + \frac{5}{40} = \frac{8}{40} \]
- Now, subtract \( \frac{5}{40} \) from both sides:
\[ A = \frac{8}{40} - \frac{5}{40} = \frac{3}{40} \]

6. **Finding Time Taken by Atul Alone**:
- If Atul's work rate is \( \frac{3}{40} \) work per day, then the time taken by Atul to complete the work alone is:
\[ \text{Time} = \frac{1 \text{ work}}{A} = \frac{1}{\frac{3}{40}} = \frac{40}{3} \text{ days} \]

### Conclusion:
Atul can complete the work alone in \( \frac{40}{3} \) days.

### Answer:
A. \( \frac{40}{3} \) days