CAT 2017 Geometry & Mensuration — Previous Year Question

$AB,\ CD$ and $EF$ are three parallel lines, in that order. Let $d_1$ and $d_2$ be the distances from $CD$ to $AB$ and $EF$ respectively. $d_1$ and $d_2$ are integers, where $d_1:d_2=2:1$. $P$ is a point on $AB$, $Q$ and $S$ are points on $CD$ and $R$ is a point on $EF$. If the area of the quadrilateral $PQRS$ is $30$ square units, what is the value of $QR$ when value of $SR$ is the least?