A and B together can complete a piece of work in 12 days, while B and C together can complete the same work in 15 days. A and C together can complete the work in 20 days. If all three work together, in how many days will they complete the work?

Let the total work be the LCM of 12, 15, and 20, which is 60 units. Work rate of A and B together = 60 / 12 = 5 units/day. Work rate of B and C together = 60 / 15 = 4 units/day. Work rate of A and C together = 60 / 20 = 3 units/day. Adding all three equations: (A + B) + (B + C) + (A + C) = 5 + 4 + 3 = 12 units/day. Twice the combined work rate of all three (A + B + C) = 12. Work rate of A + B + C = 12 / 2 = 6 units/day. Time taken to complete the work = Total work / Combined rate = 60 / 6 = 10 days. Correct answer: a) 10