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    Question

    The product of two positive integers is 1620. If their

    HCF is 9 and their sum is 81, then find the difference between the numbers.
    A 3 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 9 Correct Answer Incorrect Answer
    D 12 Correct Answer Incorrect Answer

    Solution

    Let the numbers be 9a and 9b

    Then:
    9a × 9b = 1620 ⇒ ab = 20 ...............(1)
    9a + 9b = 81 ⇒ a + b = 9

    Put a = (9 - b) in (1):
    (9 - b) × b = 20
    ⇒ 9b - b² = 20
    ⇒ b² - 9b + 20 = 0
    ⇒ b² - 4b - 5b + 20 = 0
    ⇒ b(b - 4) - 5(b - 4) = 0
    ⇒ (b - 4)(b - 5) = 0

    So, b = 4 or 5
    Then, numbers are 36 and 45
    Required difference = 9

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