AMC 12 2017b Problem 10

At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

\textbf{(A)}\ 10% \textbf{(B)}\ 12% \textbf{(C)}\ 20% \textbf{(D)}\ 25% \textbf{(E)}\ 33\frac{1}{3}%