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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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