What does this ratio mean?: percent treated or removed / percent remaining

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I have found this function in several math textbooks:

$$ C(p)=\frac{80000p}{100-p} $$

It represents the cost C(p) to remove the percent p of impurities from coal. The function shows that as we try to remove a higher percentage of impurities, the cost goes up faster and faster, and it is impossible (mathematically, anyway) to remove 100% of the impurities because we approach infinity there--we have an asymptote.

I am trying to understand what this expression

$$ \frac{p}{100-p} $$

represents.

When p is 1, it's 1/99. When p is 50, it's 1, when p is 99 it's 99. I have found this expression in a few other models. Is there a name for it? What is it doing?