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      Question

      Three positive numbers are in the ratio 2:3:4. If the sum

      of their squares is 2349, what is the average of the two largest numbers?
      A 11.5 Correct Answer Incorrect Answer
      B 21.5 Correct Answer Incorrect Answer
      C 31.5 Correct Answer Incorrect Answer
      D 45.5 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the three numbers be 2x, 3x and 4x, respectively.

      ATQ;

      (2x)┬▓ + (3x)┬▓ + (4x)┬▓ = 2349

      Or, 4x┬▓ + 9x┬▓ + 16x┬▓ = 2349

      Or, 29x┬▓ = 2349

      Or, x┬▓ = 81

      So, x = 9 (Since, numbers are positive therefore we can discard the negative root)

      So, required average = {(3 X 9) + (4 X 9) } ├╖ 2 = (63/2) = 31.5

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