A and B together can complete a piece of work in 12

Solution

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