2017 AMC 12B 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\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%

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