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    Question

    The HCF and LCM of two numbers, A and B, are 9 and 162,

    respectively. The difference between these two numbers is 27. Find their sum.
    A 81 Correct Answer Incorrect Answer
    B 90 Correct Answer Incorrect Answer
    C 55 Correct Answer Incorrect Answer
    D 60 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,
    HCF (A, B) = 9
    LCM (A, B) = 162
    We know that,
    HCF (A, B) × LCM (A, B) = A × B
    Also, A – B = 27
    Or, B = A – 27
    ATQ:
    A × (A – 27) = 9 × 162
    Or, A² – 27A = 1458
    Or, A² – 27A – 1458 = 0
    Or, A² – 54A + 27A – 1458 = 0
    Or, A(A – 54) + 27(A – 54) = 0
    Or, (A – 54)(A + 27) = 0
    So, A = 54 or A = -27
    Since, A cannot be negative, we discard A = -27.
    So, A = 54
    And, B = 54 – 27 = 27
    Therefore, required sum = (54 + 27) = 81

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