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    Question

    ‘P’ alone can paint a house in 18 days, while

    ‘P’ and ‘Q’ together can do it in 12 days. If ‘Q’ started the work and left after 6 days, how many days will ‘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 ‘P’ = 36 ÷ 18 = 2 units/day

    Combined efficiency of ‘P’ and ‘Q’ = 36 ÷ 12 = 3 units/day

    So, efficiency of ‘Q’ alone = 3 – 2 = 1 unit/day

    Work done by ‘Q’ in 6 days = 1 × 6 = 6 units

    Remaining work = 36 – 6 = 30 units

    Time taken by ‘P’ alone = 30 ÷ 2 = 15 days

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