A and B together can do a piece of work in 20 days. B and C together can do the same of work in 25 days. C and A together can do the same work in 15 days. In how many days A alone can do the same work?

Work done by A & B together = 20 Work done by B & C together = 25 Work done by C & A together = 15 Total work done A, B & C = LCM of 20, 25 & 15 = 300 units Efficiency of A & B together = 300/20 = 15 Efficiency of  B & C together = 300/25 = 12 Efficiency of  C & A together = 300/15 = 20 ⇒ 2(A + B + C) = 47 (Efficiency) ⇒ A + B + C = 23.5      ---- (1) ⇒ B + C = 12      ---- (2) From (1) and (2) ⇒ A = 11.5 ⇒ A alone can do the same work = total work/efficiency of A ⇒ A alone can do the same work = 300/11.5 = 600/23 days ∴ A alone can do the same work in 600/23 days