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    Question

    Worker β€˜P’ can complete a job in 30 days, and

    together with β€˜Q’, they can finish it in 12 days. If β€˜Q’ worked alone for 15 days and then stopped, how long will β€˜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 β€˜P’ = 60 Γ· 30 = 2 units/day
    Combined efficiency of β€˜P’ and β€˜Q’ = 60 Γ· 12 = 5 units/day
    So, efficiency of β€˜Q’ = 5 – 2 = 3 units/day
    So, work done by β€˜Q’ alone in 15 days = 3 Γ— 15 = 45 units
    Remaining work = 60 – 45 = 15 units
    Time taken by 'P' alone to complete the remaining work = 15 Γ· 2 = 7.5 days

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