AMC 8 2011 Problem 13

Two congruent squares, $ABCD$ and $PQRS$, have side length $15$. They overlap to form the $15$ by $25$ rectangle $AQRD$ shown. What percent of the area of rectangle $AQRD$ is shaded?

$\textbf{(A)}\ 15 \textbf{(B)}\ 18 \textbf{(C)}\ 20 \textbf{(D)}\ 24 \textbf{(E)}\ 25$