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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 18 days, 15 days and 10 days respectively. Find the ratio of the efficiencies of A, B and C, respectively.
      A 4:5:7 Correct Answer Incorrect Answer
      B 5:6:6 Correct Answer Incorrect Answer
      C 4:1:5 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 90 units (LCM of 18, 15 and 10)
      Amount of work done by A and B together in one day = 90/18 = 5 units
      Amount of work done by B and C together in one day = 90/15 = 6 units
      Amount of work done by A and C together in one day = 90/10 = 9 units
      Amount of work done by A, B and C together in one day = (5 + 6 + 9)/2 = 10 units
      Amount of work done by A alone in one day = 10 – 6 = 4 units
      Amount of work done by B alone in one day = 10 – 9 = 1 units
      Amount of work done by C alone in one day = 10 – 5 = 5 units
      So the desired ratio = 4:1:5

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