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      Question

      A, B, and C can complete a task individually in 45, 35,

      and 63 days respectively. They start working together, but A leaves 24 days before the work is completed, and B leaves 10 days after A leaves. How many total days does it take to finish the work?
      A 25 days Correct Answer Incorrect Answer
      B 27 days Correct Answer Incorrect Answer
      C 29 days Correct Answer Incorrect Answer
      D 31 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let total amount of work = 315 units (LCM of 45, 35 and 63)

      Amount of work done by A in one day = 315/45 = 7 units

      Amount of work done by B in one day = 315/35 = 9 units

      Amount of work done by C in one day = 315/63 = 5 units

      Let total time taken to complete the whole work is ‘x’ days

      According to question;

      5 × x + 9 × (x – 14) + 7 × (x – 24) = 315

      Or, 21x = 315 + 168 + 126

      Or, 21x = 609

      Or, x = 29

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