In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $\frac{AP}{2} = \frac{PQ}{5} = \frac{QB}{11}$ and $\frac{AR}{8} = \frac{RC}{13},$ then find $\frac{[QBC]}{[CRQ]}.$
+1911 
