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    Question

    Worker ‘P’ can complete a job in 30 days, and

    together with ‘Q’, they can finish it in 12 days. If ‘Q’ worked alone for 15 days and then stopped, how long will ‘P’ take to finish the remaining work?
    A 2.5 days Correct Answer Incorrect Answer
    B 40 days Correct Answer Incorrect Answer
    C 7.5 days Correct Answer Incorrect Answer
    D 16 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total work = 60 units {L.C.M of 30 and 12}
    Then, efficiency of ‘P’ = 60 ÷ 30 = 2 units/day
    Combined efficiency of ‘P’ and ‘Q’ = 60 ÷ 12 = 5 units/day
    So, efficiency of ‘Q’ = 5 – 2 = 3 units/day
    So, work done by ‘Q’ alone in 15 days = 3 × 15 = 45 units
    Remaining work = 60 – 45 = 15 units
    Time taken by 'P' alone to complete the remaining work = 15 ÷ 2 = 7.5 days

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