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    Question

    The combined total of two numbers is 105. Their LCM and HCF

    are 315 and 5 respectively. What is the smaller number?
    A 54 Correct Answer Incorrect Answer
    B 45 Correct Answer Incorrect Answer
    C 32 Correct Answer Incorrect Answer
    D 28 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the smaller number = ‘x’

    Greater number = (105 – x)

    Product of numbers = LCM × HCF

    Or, x(105 – x) = 5 × 315

    Or, 105x – x² = 1575

    Or, x² – 105x + 1575 = 0

    Or, x² – 60x – 45x + 1575 = 0

    Or, x(x – 60) – 45(x – 60) = 0

    Or, (x – 60)(x – 45) = 0

    So, smaller number = 45

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