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    Question

    β€˜P’ and β€˜Q’ can complete a project in 45 days

    and 60 days respectively while β€˜P’, β€˜Q’ and β€˜R’ together can complete the same project in 15 days. Find the time taken by β€˜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 β€˜P’ in one day = 180/45 = 4 units Amount of work done by β€˜Q’ in one day = 180/60 = 3 units Amount of work done by β€˜P’, β€˜Q’ and β€˜R’ in one day = 180/15 = 12 units Amount of work done by β€˜R’ in one day = 12 – 4 – 3 = 5 units Desired time = (0.50 Γ— 180)/5 = 18 days

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