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    Question

    The HCF and LCM of two numbers, A and B, are 15 and 225,

    respectively. Additionally, the difference between the two numbers is 35. Find the sum of these two numbers.
    A 75 Correct Answer Incorrect Answer
    B 90 Correct Answer Incorrect Answer
    C 115 Correct Answer Incorrect Answer
    D 56 Correct Answer Incorrect Answer

    Solution

    ATQ,
    HCF (A, B) = 15
    LCM (A, B) = 225
    We know that,
    HCF (A, B) × LCM (A, B) = A × B
    Also, A – B = 35
    Or, B = A – 35
    ATQ:
    A × (A – 35) = 15 × 225
    Or, A² – 35A = 3375
    Or, A² – 35A – 3375 = 0
    Or, A² – 75A + 40A – 3375 = 0
    Or, A(A – 75) + 40(A – 75) = 0
    Or, (A – 75)(A + 40) = 0
    So, A = 75 or A = -40
    Since, A cannot be negative, we discard A = -40.
    So, A = 75
    And, B = 75 – 35 = 40
    Therefore, required sum = (75 + 40) = 115

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