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    Question

    The LCM and HCF of two numbers is 192 and 16 respectively.

    If the sum of the number is 112, then find the difference between the numbers.
    A 16 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 24 Correct Answer Incorrect Answer
    D 14 Correct Answer Incorrect Answer

    Solution

    We know that, LCM X HCF = product of the numbers

    Let the numbers are 'a' and 'b'.

    So, a X b = 192 X 16

    So, ab = 3072........(I)

    Given, a + b = 112

    From equation (I) ,

    Or, 'a' = (3072/b)

    So, (3072/b) + b = 112

    So, 3072 + b 2  = 112b

    Or, b 2  - 112b + 3072 = 0

    Or, b 2  - 64b - 48b + 3072 = 0

    So, 'b' = 48 or 64

    When, 'b' = 48

    So, 'a' = (3072/48) = 64

    When, 'b' = 64

    So, 'a' = (3072/64) = 48

    Therefore, required difference = 64 - 48 = 16

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