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    Question

    In 5 years from now, the ratio of ages of P and Q will

    be 9:5. If age of P after 15 years is 150% more than age of Q 12 years ago, find the difference between their current ages.
    A 66 yrs Correct Answer Incorrect Answer
    B 24 yrs Correct Answer Incorrect Answer
    C 60 yrs Correct Answer Incorrect Answer
    D 54 yrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let present ages be P = p, Q = q

    (p + 5)/(q + 5) = 9/5

    => 5(p + 5) = 9(q + 5)

    => 5p + 25 = 9q + 45

    => 5p = 9q + 20 ...(1)

    150% more means 2.5 times

    P after 15 years = 2.5 × (Q 12 years ago)

    => p + 15 = 2.5(q - 12)

    => p + 15 = 2.5q - 30

    => p = 2.5q - 45

    Multiply by 2: 2p = 5q - 90 ...(2)

    Now use (1):

    5p = 9q + 20

    Multiply by 2: 10p = 18q + 40 ...(3)

    From (2): 2p = 5q - 90

    Multiply by 5: 10p = 25q - 450 ...(4)

    Equate (3) and (4):

    18q + 40 = 25q - 450

    490 = 7q

    q = 70

    Put q = 70 in (1):

    5p = 9(70) + 20 = 650

    p = 130

    Difference = p - q = 130 - 70 = 60

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