If the same number be added to the numbers $5, 11, 15$ and $31$ , the resulting numbers are in proportion. Find the number.

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Solution

Let The number be $x$
$\frac{5 + x}{11 + x} = \frac{15 + x}{31 + x}$
$\Rightarrow 155 + x^{2} + 36 x = 165 + x^{2} + 26 x$
$10 x = 10$
$x = 1$
$∴$ Numbers are $5 + 1 = 6$ , $11 + 1 = 12$
$15 + 1 = 16$ , $31 + 1 = 32$ .

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