A and B together can do a piece of work in 8 days, but A alone can do it in 12 days. How manydays would B alone take to do the same work?

Sure, let's solve this step by step:

Step 1: First, we need to find out how much work A and B can do in a day together. Since they can complete the work in 8 days, they can do 1/8 of the work in a day.

Step 2: Similarly, we can find out how much work A can do in a day alone. Since A can complete the work in 12 days, A can do 1/12 of the work in a day.

Step 3: Now, to find out how much work B can do in a day, we subtract the work done by A from the work done by A and B together. So, B can do (1/8 - 1/12) of the work in a day. Simplifying this, we get that B can do 1/24 of the work in a day.

Step 4: Finally, to find out how many days B would take to complete the work alone, we take the reciprocal of the work B can do in a day. So, B would take 24 days to complete the work alone.