A and B together, B and C together and A and C together can complete a piece of work in 11 days, 20 days and 12 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.

Let, the total work be 660 units (LCM of 11, 20 and 12) Amount of work done by A and B together in one day = 660/11 = 60 units Amount of work done by B and C together in one day = 660/20 = 33 units Amount of work done by A and C together in one day = 660/12 = 55 units Amount of work done by A, B and C together in one day = (60 + 33 + 55)/2 = 74 units Amount of work done by A alone in one day = 74 – 33 = 41 units Amount of work done by B alone in one day = 74 – 55 = 19 units Amount of work done by C alone in one day = 74 – 60 = 14 units So the desired ratio = 41:19:14