1986 AHSME Problem 20

Suppose x and y are inversely proportional and positive. If x increases by p\%, then y decreases by

\textbf{(A)}\ p\%\qquad \textbf{(B)}\ \frac{p}{1+p}\%\qquad \textbf{(C)}\ \frac{100}{p}\%\qquad \textbf{(D)}\ \frac{p}{100+p}\%\qquad \textbf{(E)}\ \frac{100p}{100+p}\%

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.