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    Question

    ‘P’ and ‘Q’ can complete a project in 45 days

    and 60 days respectively while ‘P’, ‘Q’ and ‘R’ together can complete the same project in 15 days. Find the time taken by ‘R’ alone to complete 50% of the work.
    A 12 days Correct Answer Incorrect Answer
    B 18 days Correct Answer Incorrect Answer
    C 10 days Correct Answer Incorrect Answer
    D 22 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ Let total amount of work = 180 units (LCM of 45 and 60) Amount of work done by ‘P’ in one day = 180/45 = 4 units Amount of work done by ‘Q’ in one day = 180/60 = 3 units Amount of work done by ‘P’, ‘Q’ and ‘R’ in one day = 180/15 = 12 units Amount of work done by ‘R’ in one day = 12 – 4 – 3 = 5 units Desired time = (0.50 × 180)/5 = 18 days

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