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    Question

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

    of their squares is 2349. The average of the largest and the second largest number is:
    A 30 Correct Answer Incorrect Answer
    B 27.5 Correct Answer Incorrect Answer
    C 31.5 Correct Answer Incorrect Answer
    D 22.5 Correct Answer Incorrect Answer

    Solution

    Let the three numbers be 2x, 3x and 4x, respectively.ATQ;(2x)┬а2┬а+ (3x)┬а2┬а+ (4x)┬а2┬а= 2349Or, 4x2┬а+ 9x2┬а+ 16x2┬а= 2349Or, 29x2┬а= 2349Or, x2┬а= 81So, 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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