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    Question

    The product of two positive integers is 1400. If their HCF

    is 5 and their sum is 75, then find the difference between the numbers.
    A 2 Correct Answer Incorrect Answer
    B 3 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 5 Correct Answer Incorrect Answer
    E 15 Correct Answer Incorrect Answer

    Solution

    Let the numbers be 5a and 5b

    Then:
    5a × 5b = 1400 ⇒ ab = 56 ...............(1)
    5a + 5b = 75 ⇒ a + b = 15

    Put a = (15 - b) in (1):
    (15 - b) × b = 56
    ⇒ 15b - b² = 56
    ⇒ b² - 15b + 56 = 0
    ⇒ b² - 7b - 8b + 56 = 0
    ⇒ b(b - 7) - 8(b - 7) = 0
    ⇒ (b - 7)(b - 8) = 0

    So, b = 8 or 7
    Then, numbers are 40 and 35
    Required difference = 5

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