A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

The correct answer is: 13 1/2 days.

Let’s say that the total work can be represented as W.
Step 1 of 3:
It is given that B can do the whole work(W) in 15 days.
So, work done by B in one day = ……(1)
It is given that A and B can do the work in 20 days
So, work done by A and B in one day = 
Step 2 of 3:
It is given that A and B worked together for 2 days and then A goes away.
Work done by A and B in 2 days =  = 
Work left for B after A goes away = W - Work done by A and B in 2 days
= W - 
= W - 
Work left for B after A goes away = 
Step 3 of 3:
Now, we need to find the number of days to complete  amount of work.
From equation (1) time taken by B to complete  work = 1 day
time taken by B to complete  work = 
Final Answer:
Hence, the time taken by B to complete the work after A after 2 days is 13  days.