MathNet 2012 Question 7

Let $ABCD$ be a convex quadrilateral. Let $P$ and $Q$ be points on the sides $AB$ and $AD$, respectively, such that $area(ABQ) = area(ADP) = \frac{1}{3} area(ABCD)$.
$PQ$ and the diagonal $AC$ meet at the point $R$.
Calculate the ratio $\frac{AR}{RC}$.

Illustrative configuration only.