Consider three positive numbers that form a ratio of 2:3:4. If the sum of the squares of these numbers is 2349, what is the average of the largest and the second largest numbers?
Let the three numbers be 2x, 3x and 4x, respectively. ATQ; (2x) 2 + (3x) 2 + (4x) 2 = 2349 Or, 4x2 + 9x2 + 16x2 = 2349 Or, 29x2 = 2349 Or, x2 = 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 Hence, option c.
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