$1 . x$ and $y$ are positive numbers and are inversely proportional. If $x$ increases by $p \%$, let the percentage decrease in $y$ be $q$ \%. Then the value of $q$ is ( ).
(A) $\frac{100 p}{1+p \%}$
(B) $\frac{100}{p \%}$
(C) $\frac{p}{100+p}$
(D) $\frac{100 p}{100+p}$
-、1.D.
Since $x, y$ are inversely proportional, we can set $y=\frac{k}{x}$, then we have
$$
(1-q \%) y=\frac{k}{(1+p \%) x}, q=\frac{100 p}{100+p} .
$$