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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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