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      Question

      'P', 'Q', and 'R' can complete a job in 60, 90, and 120

      days respectively. They begin together, but 'P' leaves 10 days before the work is done and 'Q' leaves 5 days before completion. How long did the work take? (Calculate approximate value)
      A 65 days Correct Answer Incorrect Answer
      B 13 days Correct Answer Incorrect Answer
      C 78 days Correct Answer Incorrect Answer
      D 34 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work be 360 units (LCM of 60, 90, 120)

      Efficiency of 'P' = 360 / 60 = 6 units/day

      Efficiency of 'Q' = 360 / 90 = 4 units/day

      Efficiency of 'R' = 360 / 120 = 3 units/day

      Let the time taken = n days

      (6 + 4 + 3)(n - 10) + (4 + 3)(5) + 3(5) = 360

      Or, 13n - 130 + 35 + 15 = 360

      Or, 13n = 440

      So, n = 440 / 13 = 33.84 ≈ 34 days

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