If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

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Solution

The correct option is B
14

Let the numbers be 3x, 2x and 5x.

Then, $9 x^{2} + 4 x^{2} + 25 x^{2} = 1862$

$\Rightarrow 38 x^{2} = 1862$

$\Rightarrow x^{2} = 49$

$\Rightarrow x = 7$

Thus, middle number = 2x = 14.

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