jmc

Construct the altitude of $△PQT$ from $P$ to $QT$. Let the length of the altitude be $h$. Note that this altitude of $△PQT$ is also the altitude of $△PTR$. The ratio of the area of $△PQT$ to the area of $△PTR$ is $$\frac{\frac{1}{2}\times QT\times h}{\frac{1}{2}\times TR\times h}=\frac{QT}{TR}=\frac{6}{10}=\frac{3}{5}.$$Therefore, our final answer is $\boxed{3:5}$.