SEAMO 2027 - Paper D - SET 09 - Self-study Question 12

In triangle $ABC$, $D$ lies on $BA$ with $BD:DA=1:2$, and $E$ lies on $CB$ with $CE:EB=1:4$. Segments $DC$ and $AE$ meet at $F$. Express $CF:FD$ using two relatively prime positive integers.