you have two numbers $x$ and $y=\dfrac{px}{100}$

The arithmetic mean is $\dfrac{x+y}{2}=\dfrac{100x+px}{2\cdot 100}=\dfrac{(100+p)x}{200}$

The geometric mean is

$\sqrt{xy}=\sqrt{\dfrac{px^2}{100}}=\dfrac{x\sqrt{ p}}{10}$

I don't really know how to interpret your actual question, but given these two means you can figure out the ratio you are after.