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      Question

      Worker ‘P’ can complete a job in 30 days, and

      together with ‘Q’, they can finish it in 12 days. If ‘Q’ worked alone for 15 days and then stopped, how long will ‘P’ take to finish the remaining work?
      A 2.5 days Correct Answer Incorrect Answer
      B 40 days Correct Answer Incorrect Answer
      C 7.5 days Correct Answer Incorrect Answer
      D 16 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the total work = 60 units {L.C.M of 30 and 12}
      Then, efficiency of ‘P’ = 60 ÷ 30 = 2 units/day
      Combined efficiency of ‘P’ and ‘Q’ = 60 ÷ 12 = 5 units/day
      So, efficiency of ‘Q’ = 5 – 2 = 3 units/day
      So, work done by ‘Q’ alone in 15 days = 3 × 15 = 45 units
      Remaining work = 60 – 45 = 15 units
      Time taken by 'P' alone to complete the remaining work = 15 ÷ 2 = 7.5 days

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