Important concept: k% = \(\frac{k}{100}\)

So we can take our given information and write the following equation: \(\frac{\frac{1}{x}}{100}y = \frac{9y}{100}x\)

Simplify: \(\frac{y}{100x }= \frac{9xy}{100}\)

Cross multiply: \(900x^2y = 100y\)

Divide both sides by \(100y\) to get: \(9x^2 = 1\)

Divide both sides by \(9\) to get: \(x^2 = \frac{1}{9}\), which means \(x = \frac{1}{3}\) or \(x = -\frac{1}{3}\)

Since we're told \(x\) is positive, we know that \(x = \frac{1}{3}\)

Answer: B