$$\begin{gathered} \begin{array}{l}\text{ Here, }\\ \Rightarrow x\text{\% of 500 = y\% of 300}\\ \\ \text{It can also be written as}\\ \\ \Rightarrow \frac{x}{35}\times 500=\frac{y}{100}\times 300\Rightarrow 5x=3y\\ \\ \Rightarrow \text{ 5}x-3y\text{\hspace{0.17em}=0 \hspace{0.17em}\hspace{0.17em}\_\_\_(i)}\\ \\ \Rightarrow x=\frac{3}{5}y\\ \\ \text{Again, x\% of y\% of 200 = 60}\\ \\ \Rightarrow \frac{x}{100}\times \frac{y}{100}\times 200=60\\ \\ \Rightarrow xy=\frac{60\times 100}{2}\\ \\ \Rightarrow xy=3000\\ \\ \text{Putting \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x\frac{3}{5}y \Rightarrow \frac{3}{5}y\times y=3000\end{array} \\ \Rightarrow y^2=1000\times 5 \\ \Rightarrow y =50\sqrt{2} \\ and \Rightarrow x=\frac{3}{5}\times 50\sqrt{2}=30\sqrt{2} \end{gathered}$$

Hence, Option D is correct.