If A and B together can do a piece of work in 20 days, and A alone can do the same work in 30 days, then in how many days can B alone complete the same work?

Time take by A and B together can do a piece of work = 20 days, 

Time take by A alone to do the same work = 30 days 

Work rate of A alone:$$\frac{1}{\text{Days taken by A}}​$$​​

Work rate of B alone:$$\frac{1}{\text{Days taken by B}}$$​​

Work rate of A and B together: $$\frac{1}{\text{Days taken by A and B together}}$$​​

​$$\frac{1}{\text{Days taken by B}} = \frac{1}{\text{Days taken by A and B together}} - \frac{1}{\text{Days taken by A}}$$  ​

Therefore, time taken by B alone to complete the work is 60 days.