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      Question

      β€˜M’ and β€˜N’ together can finish a piece of work

      in 22 days. If β€˜M’ alone can complete it in 55 days, how many days will β€˜N’ alone take?
      A 133/22 days Correct Answer Incorrect Answer
      B 111/21 days Correct Answer Incorrect Answer
      C 110/3 days Correct Answer Incorrect Answer
      D 120/7 days Correct Answer Incorrect Answer

      Solution

      Let the total work be LCM (22, 55) = 110 units.
      Combined efficiency of β€˜M’ and β€˜N’ = 110 Γ· 22 = 5 units/day
      Efficiency of β€˜M’ = 110 Γ· 55 = 2 units/day
      Efficiency of β€˜N’ = 5 βˆ’ 2 = 3 units/day
      Time taken by β€˜N’ alone = 110 Γ· 3 = (110/3) days

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