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      Question

      A and B together, B and C together and A and C

      together can complete a piece of work in 13 days, 10 days and 14 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.
      A 19:26:16 Correct Answer Incorrect Answer
      B 41:19:14 Correct Answer Incorrect Answer
      C 26:29:4 Correct Answer Incorrect Answer
      D 47:15:4 Correct Answer Incorrect Answer
      E 22:48:43 Correct Answer Incorrect Answer

      Solution

      Let, the total work be 910 units (LCM of 13, 10 and 14)
      Amount of work done by A and B together in one day = 910/13 = 70 units
      Amount of work done by B and C together in one day = 910/10 = 91 units
      Amount of work done by A and C together in one day = 910/14 = 65 units
      Amount of work done by A, B and C together in one day = (70 + 91 + 65)/2 = 113 units
      Amount of work done by A alone in one day = 113 – 91 = 22 units
      Amount of work done by B alone in one day = 133 – 65 = 48 units
      Amount of work done by C alone in one day = 133 – 70 = 43 units
      So the desired ratio = 22:48:43

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