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      Question

      ‘D’ alone can finish a job in 50 days, while ‘D’

      and ‘E’ together can complete it in 20 days. If ‘E’ worked alone for 22 days and then left, how many days will ‘D’ take to complete 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 17 days Correct Answer Incorrect Answer

      Solution

      Let the total work = 100 units {L.C.M of 50 and 20}
      Then, efficiency of ‘D’ = 100 ÷ 50 = 2 units/day
      Combined efficiency of ‘D’ and ‘E’ = 100 ÷ 20 = 5 units/day
      So, efficiency of ‘E’ = 5 – 2 = 3 units/day
      So, work done by ‘E’ alone in 22 days = 3 × 22 = 66 units
      Remaining work = 100 – 66 = 34 units
      Time taken by 'D' alone to complete the remaining work = 34 ÷ 2 = 17 days

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