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      Question

      The product of two positive integers is 2646. If their

      HCF is 7 and their sum is 105, then find the difference between the numbers.
      A 11 Correct Answer Incorrect Answer
      B 16 Correct Answer Incorrect Answer
      C 21 Correct Answer Incorrect Answer
      D 26 Correct Answer Incorrect Answer

      Solution

      Let the numbers be 7a and 7b

      Then:
      7a × 7b = 2646 ⇒ ab = 54 ...............(1)
      7a + 7b = 105 ⇒ a + b = 15

      Put a = (15 - b) in (1):
      (15 - b) × b = 54
      ⇒ 15b - b² = 54
      ⇒ b² - 15b + 54 = 0
      ⇒ b² - 6b - 9b + 54 = 0
      ⇒ b(b - 6) - 9(b - 6) = 0
      ⇒ (b - 6)(b - 9) = 0

      So, b = 6 or 9
      Then, numbers are 42 and 63
      Required difference = 21

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