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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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