A and B together, B and C together and A and C together can complete a piece of work in 14 days, 15 days and 18 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.

Let, the total work be 630 units (LCM of 14, 15 and 18) Amount of work done by A and B together in one day = 630/14 = 45 units Amount of work done by B and C together in one day = 630/15 = 42 units Amount of work done by A and C together in one day = 630/18 = 35 units Amount of work done by A, B and C together in one day = (45 + 42 + 35)/2 = 61 units Amount of work done by A alone in one day = 61 – 42 = 19 units Amount of work done by B alone in one day = 61 – 35 = 26 units Amount of work done by C alone in one day = 61 – 45 = 16 units So the desired ratio = 19:26:16