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    Question

    The HCF and LCM of two numbers, A and B, are 14 and 196,

    respectively. The difference between these two numbers is 28. Find their sum.
    A 88 Correct Answer Incorrect Answer
    B 84 Correct Answer Incorrect Answer
    C 55 Correct Answer Incorrect Answer
    D 60 Correct Answer Incorrect Answer

    Solution

    ATQ,
    HCF (A, B) = 14
    LCM (A, B) = 196
    We know that,
    HCF (A, B) × LCM (A, B) = A × B
    Also, A – B = 28
    Or, B = A – 28
    ATQ:
    A × (A – 28) = 14 × 196
    Or, A² – 28A = 2744
    Or, A² – 28A – 2744 = 0
    Or, A² – 56A + 28A – 2744 = 0
    Or, A(A – 56) + 28(A – 56) = 0
    Or, (A – 56)(A + 28) = 0
    So, A = 56 or A = -28
    Since, A cannot be negative, we discard A = -28.
    So, A = 56
    And, B = 56 – 28 = 28
    Therefore, required sum = (56 + 28) = 84

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