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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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