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      Question

      β€˜X’ and β€˜Y’ are capable of finishing a work in 9

      days and 12 days respectively. They worked together for 3 days. Find the number of days β€˜Y’ alone would take to complete the leftover work.
      A 2 days Correct Answer Incorrect Answer
      B 7 days Correct Answer Incorrect Answer
      C 4 days Correct Answer Incorrect Answer
      D 5 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work be 36 units (LCM of 9 and 12)

      Efficiency of β€˜X’ = 36 Γ· 9 = 4 units/day

      Efficiency of β€˜Y’ = 36 Γ· 12 = 3 units/day

      Work done by β€˜X’ and β€˜Y’ together in 3 days = 3 Γ— (4 + 3) = 21 units

      Remaining work = 36 – 21 = 15 units

      Time taken by β€˜Y’ to finish the remaining work = 15 Γ· 3 = 5 days

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