If you assume _one_ of the answers must be the correct one, here's a way to see that it can only be (E):
$\triangle SMN$ is similar to $\triangle SQR$ and of half its dimensions, therefore a quarter of its area. $\triangle SQR$ is strictly _smaller_ than $\triangle NQR$, which, because $N$ is the midpoint of $PQ$, is half the area of $\triangle PQR$. The area of $\triangle SMN$ is therefore strictly smaller than one-eight the area of $\triangle PQR$.
The only ratio amongst the proffered answers that meets this condition is the ratio $1{:}12$ of (E).