Let the original fraction be $\frac{x}{y}$

Then, $$\begin{gathered} \Rightarrow \frac{x+x\times {\displaystyle \frac{240}{100}}}{y-y\times {\displaystyle \frac{50}{100}}}=\frac{17}{6} \\ \Rightarrow \frac{{\displaystyle x+\frac{12x}{5}}}{y-{\displaystyle \frac{y}{2}}}=\frac{17}{6} \\ \Rightarrow \frac{{\displaystyle \frac{17x}{5}}}{{\displaystyle \frac{y}{2}}}=\frac{17}{6} \\ \Rightarrow \frac{{\displaystyle 17x}}{5}\times \frac{2}{y}=\frac{17}{6} \\ \Rightarrow \frac{{\displaystyle 34x}}{5y}=\frac{17}{6} [by cross multipllication] \\ \Rightarrow 204x=85y \\ \Rightarrow \frac{x}{y}=\frac{85}{204}=\frac{5}{12} \\ \Rightarrow \frac{x}{y}=\frac{5}{12} \end{gathered}$$

Hence, option C is correct.