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    Question

    Two numbers add up to 98. If the LCM of the numbers is 315

    and the HCF is 9, find the smaller of the two numbers.
    A 58 Correct Answer Incorrect Answer
    B 45 Correct Answer Incorrect Answer
    C 32 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the smaller number = ‘x’

    Greater number = (98 – x)

    Product of the numbers = product of their LCM and HCF

    Or, x(98 – x) = 9 × 315

    Or, 98x – x² = 2835

    Or, x² – 98x + 2835 = 0

    Or, x² – 63x – 35x + 2835 = 0

    Or, x(x – 63) – 45(x – 63) = 0

    Or, (x – 63)(x – 45) = 0

    Or, x = 63, 45

    So, smaller number = 45

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