When one ounce of water is added to a mixture of acid and water, the new mixture is $20\%$ acid. When one ounce of acid is added to the new mixture, the result is $33\frac13\%$ acid. The percentage of acid in the original mixture is
$\textbf{(A)}\ 22\% \qquad \textbf{(B)}\ 24\% \qquad \textbf{(C)}\ 25\% \qquad \textbf{(D)}\ 30\% \qquad \textbf{(E)}\ 33\frac13 \%$
Let $a$ be the original number of ounces of acid and $w$ be the original number of ounces of water.  We can write two equations since we know the percentage of acid after some water and acid.
\[\frac{a}{a+w+1} = \frac{1}{5}\]
\[\frac{a+1}{a+w+2} = \frac{1}{3}\]
Cross-multiply to get rid of the fractions.
\[5a = a+w+1\]
\[3a+3=a+w+1\]
Solve the system to get $a=1$ and $w=3$.  The percentage of acid in the original mixture is $\tfrac{1}{1+3} = \boxed{\textbf{(C)}\ 25\%}$.