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      Question

      The product of two positive integers is 1400. If their HCF

      is 5 and their sum is 75, then find the difference between the numbers.
      A 2 Correct Answer Incorrect Answer
      B 3 Correct Answer Incorrect Answer
      C 4 Correct Answer Incorrect Answer
      D 5 Correct Answer Incorrect Answer
      E 15 Correct Answer Incorrect Answer

      Solution

      Let the numbers be 5a and 5b

      Then:
      5a × 5b = 1400 ⇒ ab = 56 ...............(1)
      5a + 5b = 75 ⇒ a + b = 15

      Put a = (15 - b) in (1):
      (15 - b) × b = 56
      ⇒ 15b - b² = 56
      ⇒ b² - 15b + 56 = 0
      ⇒ b² - 7b - 8b + 56 = 0
      ⇒ b(b - 7) - 8(b - 7) = 0
      ⇒ (b - 7)(b - 8) = 0

      So, b = 8 or 7
      Then, numbers are 40 and 35
      Required difference = 5

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