Choice C is correct. Multiplying each side of the given equation by $\frac{1}{20}$ yields $\frac{1}{20} (\frac{20}{p}) = \frac{1}{20} (\frac{20}{q} - \frac{20}{r} - \frac{20}{s})$ . Distributing $\frac{1}{20}$ on each side of this equation yields $\frac{20}{20 p} = \frac{20}{20 q} - \frac{20}{20 r} - \frac{20}{20 s}$ , or $\frac{1}{p} = \frac{1}{q} - \frac{1}{r} - \frac{1}{s}$ . Adding $\frac{1}{r} + \frac{1}{s}$ to each side of this equation yields $\frac{1}{s} + \frac{1}{r} + \frac{1}{p} = \frac{1}{q}$ . Multiplying $StartFraction 1 Over s EndFraction$ by $\frac{p r}{p r}$ , $StartFraction 1 Over r EndFraction$ by $\frac{p s}{p s}$ , and $StartFraction 1 Over p EndFraction$ by $\frac{r s}{r s}$ yields $\frac{p r}{p r s} + \frac{p s}{p r s} + \frac{r s}{p r s} = \frac{1}{q}$ , which is equivalent to $\frac{p r + p s + r s}{p r s} = \frac{1}{q}$ . Since $\frac{p r + p s + r s}{p r s} = \frac{1}{q}$ , and it's given that $p$ , $q$ , $r$ , and $s$ are positive, it follows that the reciprocals of each side of this equation are also equal. Thus, $\frac{p r s}{p r + p s + r s} = \frac{q}{1}$ , or $\frac{p r s}{p r + p s + r s} = q$ . Therefore, $\frac{p r s}{p r + p s + r s}$ is equivalent to $q$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.