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      Question

      Riya completes 40% of a task in 24 days, while Siya

      finishes 30% of the same task in 27 days. Riya begins the task alone and stops after 30 days. How long will Siya take to finish the rest?
      A 45 days Correct Answer Incorrect Answer
      B 61 days Correct Answer Incorrect Answer
      C 52 days Correct Answer Incorrect Answer
      D 35 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Time taken by Riya to complete whole work = (24 / 0.40) = 60 days

      Time taken by Siya to complete whole work = (27 / 0.30) = 90 days

      Let total work = LCM of 60 and 90 = 180 units

      Efficiency of Riya = 180 / 60 = 3 units/day

      Efficiency of Siya = 180 / 90 = 2 units/day

      Work done by Riya in 30 days = 30 × 3 = 90 units

      Remaining work = 180 - 90 = 90 units

      Time taken by Siya = 90 / 2 = 45 days

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