A and B together, B and C together and A and C together can complete a piece of work in 12 days, 11 days and 12 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.

Let, the total work be 132 units (LCM of 12, 11 and 12) Amount of work done by A and B together in one day = 132/12 = 11 units Amount of work done by B and C together in one day = 132/11 = 12 units Amount of work done by A and C together in one day = 132/12 = 11 units Amount of work done by A, B and C together in one day = (11 + 12 + 11)/2 = 17 units Amount of work done by A alone in one day = 17 – 12 = 5 units Amount of work done by B alone in one day = 17 – 11 = 6 units Amount of work done by C alone in one day = 17 – 11 = 6 units So the desired ratio = 5:6:6