A and B can finish a work in 15 days B and C can finish the same work in 12 days and C and A in 20 days. If A, B and C start working alternately starting with A then in how many days work will finish?

Let total work = LCM(15, 12, 20) = 60 units. (A+B) = 60/15 = 4 units/day, (B+C) = 60/12 = 5 units/day, (C+A) = 60/20 = 3 units/day. Adding: 2(A+B+C) = 12, so A+B+C = 6 units/day. Individual rates: A = 6-5 = 1, B = 6-3 = 3, C = 6-4 = 2 units/day. Working alternately A→B→C: Cycle of 3 days = 1+3+2 = 6 units. 10 cycles (30 days) = 60 units, so work completes in exactly 30 days.