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      Question

      Amit', 'Bhanu', and 'Chintu' can finish a piece of work

      in 51 days, 85 days, and 102 days respectively. They all begin working together on the task, but 'Bhanu' stops working 19 days before the work is completed, and 'Amit' leaves 9 days before it ends. Determine the total number of days required to complete the work.
      A 45 Correct Answer Incorrect Answer
      B 24 Correct Answer Incorrect Answer
      C 60 Correct Answer Incorrect Answer
      D 34 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work be 510 units (LCM of 51, 85 and 102)

      Efficiency of 'Aman' = (510/51) = 10 units/day

      Efficiency of 'Bhanu' = (510/85) = 6 units/day

      Efficiency of 'Chintu' = (510/102) = 5 units/day

      Let the time taken to complete the work be 'd' days.

      So, (10 + 6 + 5) X (d - 19) + (10 + 5) X 10 + 5 X 9 = 510

      Or, 21d - 399 + 150 + 45 = 510

      Or, 21d = 714

      Or, 'd' = 34

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