According to the question, $\frac{3+x}{4+x} = \frac{15-x}{17-x}$
$\Rightarrow (3+x)(17-x) = (4+x)(15-x)$
$\Rightarrow \require{cancel} 51-3x + 17x – {\color{Red}{\cancel{x^{2}}}} = 60 + 15x-4x – {\color{Red}{\cancel{x^{2}}}}$
$\Rightarrow 14x-11x = 60-51$
$\Rightarrow 3x = 9$
$\Rightarrow {\color{Blue}{\boxed{x = 3}}}$
Correct Answer $:\text{C}$