A and B together, B and C together and A and C together can complete a piece of work in 44 days, 33 days and 36 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.

Let, the total work be 396 units (LCM of 44, 33 and 36)

Amount of work done by A and B together in one day = 396/44 = 9 units

Amount of work done by B and C together in one day = 396/33 = 12 units

Amount of work done by A and C together in one day = 396/36 = 11 units

Amount of work done by A, B and C together in one day = (9 + 12 + 11)/2 = 16 units

Amount of work done by A alone in one day = 16 – 12 = 4 units

Amount of work done by B alone in one day = 16 – 11 = 5 units

Amount of work done by C alone in one day = 16 – 9 = 7 units

So the desired ratio = 4:5:7

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