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      Question

      β€˜P’ alone can paint a house in 18 days, while

      β€˜P’ and β€˜Q’ together can do it in 12 days. If β€˜Q’ started the work and left after 6 days, how many days will β€˜P’ take to complete the painting?
      A 20 days Correct Answer Incorrect Answer
      B 18 days Correct Answer Incorrect Answer
      C 12 days Correct Answer Incorrect Answer
      D 15 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work = 36 {L.C.M of 18 and 12}

      Efficiency of β€˜P’ = 36 Γ· 18 = 2 units/day

      Combined efficiency of β€˜P’ and β€˜Q’ = 36 Γ· 12 = 3 units/day

      So, efficiency of β€˜Q’ alone = 3 – 2 = 1 unit/day

      Work done by β€˜Q’ in 6 days = 1 Γ— 6 = 6 units

      Remaining work = 36 – 6 = 30 units

      Time taken by β€˜P’ alone = 30 Γ· 2 = 15 days

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