What number must be added to each of the numbers $10, 18, 22, 38$ to make them in proportion?

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Solution

The correct option is C ( $2$ )
Given numbers: $10, 18, 22, 38$
Let the number be $x$ .
$\Rightarrow 10 + x : 18 + x = 22 + x : 38 + x$
$\Rightarrow (10 + x) (38 + x) = (18 + x) (22 + x)$
$380 + 10 x + 38 x + x^{2} = 396 + 18 x + 22 x + x^{2}$
$48 x - 40 x = 396 - 380$
$8 x = 16$
$∴ x = 2$

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