A and B can do a piece of work in 40 days, B and C can do it in 120 days. If B alone can do it in 180 days, in how many days will A and C do it together?

Question: A and B can do a piece of work in 40 days, B and C can do it in 120 days. If B alone can do it in 180 days, in how many days will A and C do it together?

Solution:
A + B take 40 days. B alone takes 180 days.
∴ A will take 1/40 - 1/180 = 7/360 i.e. 360/7 days.

B + C take 120 days.
∴ C alone will take 1/120 - 1/180 = 1/360  360 days.

∴ A & C together will take 7/360 + 1/360 = 8/360 i.e. 360/8 = 45 days to complete the work.