OSN 2006 Problem 5

In triangle $ABC$ , $M$ is the midpoint of side $BC$ and $G$ is the centroid of triangle $ABC$ . A line $l$ passes through $G$ , intersecting line $AB$ at $P$ and line $AC$ at $Q$ , where $P\ne B$ and $Q\ne C$ . If $[XYZ]$ denotes the area of triangle $XYZ$ , show that $\frac{[BGM]}{[PAG]}+\frac{[CMG]}{[QGA]}=\frac32$ .