A and B can do a piece of work in 20 days, B and C can do it in 60 days. If B alone can do it in 90 days, in how many days will A and C do it together?

Sure, let's solve this step by step:

Step 1: Find the work done by A and B together in one day. Since A and B can complete the work in 20 days, they can do 1/20 of the work in one day.

Step 2: Similarly, find the work done by B and C together in one day. Since B and C can complete the work in 60 days, they can do 1/60 of the work in one day.

Step 3: Find the work done by B alone in one day. Since B can complete the work in 90 days, B can do 1/90 of the work in one day.

Step 4: Now, we know that (work done by A and B in one day) + (work done by B and C in one day) = (work done by A, B, and C in one day) + 2*(work done by B in one day).

So, 1/20 + 1/60 = (work done by A, B, and C in one day) + 2*(1/90).

Solving this equation gives us the work done by A, B, and C in one day as 1/15.

Step 5: We know that (work done by A, B, and C in one day) = (work done by A and C in one day) + (work done by B in one day).

So, 1/15 = (work done by A and C in one day) + 1/90.

Solving this equation gives us the work done by A and C in one day as 1/18.

Step 6: Therefore, A and C together can complete the work in 18 days.