If x% of 500 = y% of 300 and x% of y% of 200 = 60, then x = ?

Answer: Option D

$$\begin{array}{rl}& x\%\text{ of 500 }=y\%\text{ of 300}\\ & \Rightarrow \frac{x}{100}\times 500=\frac{y}{100}\times 300\\ & \Rightarrow 5x=3y\\ & \Rightarrow y=\frac{5}{3}x\\ & x\%\text{ of }y\%\text{ of 200}=60\\ & \Rightarrow \frac{x}{100}\times \frac{y}{100}\times 200=60\\ & \Rightarrow xy=3000\\ & \Rightarrow x\times \frac{5}{3}x=3000\\ & \Rightarrow x^2=3000\times \frac{3}{5}\\ & \Rightarrow x^2=1800\\ & \Rightarrow x=30\sqrt{2}\end{array}$$