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      Question

      The arithmetic mean of two values ‘a’ and ‘b’ is

      16, and their geometric mean is 10√2. Find the positive difference between the numbers, given that b > a.
      A 11 Correct Answer Incorrect Answer
      B 6 Correct Answer Incorrect Answer
      C 3 Correct Answer Incorrect Answer
      D 1 Correct Answer Incorrect Answer

      Solution

      ATQ,

      According to question;

      m + n = 13 × 2 = 26

      And, √(mn) = 6√5

      Squaring both sides we get;

      m × n = 36 × 5 = 180

      Or, n(26 – n) = 180

      Or, n² – 26n + 180 = 0

      Or, n² – 16n – 10n + 180 = 0

      Or, n(n – 16) – 10(n – 16) = 0

      Or, (n – 10)(n – 16) = 0

      Or, n = 10 (not valid) or n = 16

      So, m = 26 – 16 = 10

      So, the difference = 16 – 10 = 6

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