Correct Answer: 49 : 256

Solution :
Since $\angle A$ is common and $DE||BC$, $\triangle ADE\sim\triangle ABC$
And given: $AD:DB=7:9$
⇒ $AD:(AD+DB) = 7:(7+9)$
$\therefore AD:(AB)= 7:16$
Since $\triangle ADE\sim\triangle ABC$,
$AD:AB = DE:BC = AE:AC = 7:16$
Since $DE||BC$,
$\angle FDE= \angle FCB$ (alternate interior angles)
$\angle FED = \angle FBC$ (alternate interior angles)
And $\angle DFE = \angle CFB$ (vertically opposite angles)
So, $\triangle DEF\sim\triangle CBF$ by AAA criteria
Now, the area of similar triangles is proportional to squares of sides of triangles.
So, Area ($\triangle DEF$) : Area ($\triangle CBF$) = $DE^2:BC^2$
⇒ Area($\triangle DEF$) : Area ($\triangle CBF$) = $7^2 : 16^2$
$\therefore$ Area ($\triangle DEF$) : Area($\triangle CBF$) = 49 : 256
Hence, the correct answer is 49 : 256.