Question
Three positive numbers are in the ratio 2:3:4. The sum
of their squares is 2349. What is the average of the largest and the second largest number?Solution
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
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