AHSME 1952 Problem 34

The price of an article was increased $p\%$. Later the new price was decreased $p\%$. If the last price was one dollar, the original price was: $\textbf{(A)}\ \frac{1-p^2}{200} \textbf{(B)}\ \frac{\sqrt{1-p^2}}{100} \textbf{(C)}\ \text{one dollar} \\ \textbf{(D)}\ 1-\frac{p^2}{10000-p^2} \textbf{(E)}\ \frac{10000}{10000-p^2}$