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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 22 days, 20 days and 12 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.
      A 4:5:7 Correct Answer Incorrect Answer
      B 26:4:29 Correct Answer Incorrect Answer
      C 4:7:5 Correct Answer Incorrect Answer
      D 7:5:4 Correct Answer Incorrect Answer
      E 4:2:7 Correct Answer Incorrect Answer

      Solution

      Let, the total work be 660 units (LCM of 22, 20 and 12)
      Amount of work done by A and B together in one day = 660/22 = 30 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 = (30 + 33 + 55)/2 = 59 units
      Amount of work done by A alone in one day = 59 – 33 = 26 units
      Amount of work done by B alone in one day = 59 – 55 = 4 units
      Amount of work done by C alone in one day = 59 – 30 = 29 units
      So the desired ratio = 26:4:29

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