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      Question

      Person ‘R’ can complete a task in 60 days, and

      together with ‘S’, they can do it in 24 days. If ‘S’ worked alone for 18 days and then left, how many days will ‘R’ take to finish the remaining work?
      A 25 days Correct Answer Incorrect Answer
      B 40 days Correct Answer Incorrect Answer
      C 33 days Correct Answer Incorrect Answer
      D 16 days Correct Answer Incorrect Answer

      Solution

      Let the total work = 120 units {L.C.M of 60 and 24}
      Then, efficiency of ‘R’ = 120 ÷ 60 = 2 units/day
      Combined efficiency of ‘R’ and ‘S’ = 120 ÷ 24 = 5 units/day
      So, efficiency of ‘S’ = 5 – 2 = 3 units/day
      So, work done by ‘S’ alone in 18 days = 3 × 18 = 54 units
      Remaining work = 120 – 54 = 66 units
      Time taken by 'R' alone to complete the remaining work = 66 ÷ 2 = 33 days

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