A and B together can do a work in 15 days, if B alone can do that work in 20 days, Then how many days will A take to do same work alone?

Options

A. 60
B. 45
C. 40
D. 30

Answer

To solve the problem, we need to find out how many days A will take to complete the work alone, given that A and B together can complete the work in 15 days, and B alone can complete it in 20 days.

### Step-by-Step Solution:

1. **Determine B's Work Rate:**
Since B can complete the work in 20 days, the work done by B in one day is:
\[ \text{B's one day work} = \frac{1}{20} \]

2. **Determine A and B's Combined Work Rate:**
A and B together can complete the work in 15 days, so their combined work rate is:
\[ \text{A and B's one day work} = \frac{1}{15} \]

3. **Calculate A's Work Rate:**
To find A's work rate, we can use the combined work rate and subtract B's work rate from it:
\[ \text{A's one day work} = \text{A and B's one day work} - \text{B's one day work} \]
Substituting the values we found:
\[ \text{A's one day work} = \frac{1}{15} - \frac{1}{20} \]

4. **Finding a Common Denominator:**
The least common multiple (LCM) of 15 and 20 is 60. We can express both fractions with a denominator of 60:
\[ \frac{1}{15} = \frac{4}{60} \quad \text{and} \quad \frac{1}{20} = \frac{3}{60} \]
Now substituting back:
\[ \text{A's one day work} = \frac{4}{60} - \frac{3}{60} = \frac{1}{60} \]

5. **Calculate the Time A Takes to Complete the Work Alone:**
If A's one day work is \(\frac{1}{60}\), then A will take:
\[ \text{Time taken by A} = 60 \text{ days} \]

### Final Answer:
A can complete the same work alone in **60 days**.