(A + B) can do a piece of work in 20 days and A can do same work in 60 days. In how many days will B do this work ?

Answer

To solve the problem, we need to determine how many days B will take to complete the work alone, given the work rates of A and B together and A alone.

### Step-by-step Solution:

1. **Understand the Work Rates**:
- A and B together can complete the work in 20 days.
- A alone can complete the work in 60 days.

2. **Calculate Total Work**:
- We can assume the total work to be the least common multiple (LCM) of the days taken by A and A+B.
- LCM of 20 and 60 is 60 units of work.

3. **Calculate Work Done by A and B Together**:
- Since A and B together complete the work in 20 days, they complete:
\[ \text{Work done in one day by A and B} = \frac{60 \text{ units}}{20 \text{ days}} = 3 \text{ units/day} \]

4. **Calculate Work Done by A Alone**:
- A completes the work in 60 days, so A's work rate is:
\[ \text{Work done in one day by A} = \frac{60 \text{ units}}{60 \text{ days}} = 1 \text{ unit/day} \]

5. **Calculate Work Done by B Alone**:
- To find B's work rate, we subtract A's work rate from the combined work rate of A and B:
\[ \text{Work done in one day by B} = \text{Work done by A and B} - \text{Work done by A} \]
\[ = 3 \text{ units/day} - 1 \text{ unit/day} = 2 \text{ units/day} \]

6. **Calculate Time Taken by B to Complete the Work**:
- Now, we can find out how many days B will take to complete the total work:
\[ \text{Time taken by B} = \frac{\text{Total work}}{\text{Work done in one day by B}} = \frac{60 \text{ units}}{2 \text{ units/day}} = 30 \text{ days} \]

### Final Answer:
B will take **30 days** to complete the work alone.

---