a
$y_{1}=6 \cos \left(6 \pi t+\frac{\pi}{6}\right)$
$y_{2}=3(\sqrt{2} \sin 3 \pi t+\cos 3 \pi t)$
$=6\left[\frac{\sqrt{3}}{2} \sin 3 \pi t+\frac{1}{2} \cos 3 \pi t\right]$
$6\left[\sin \left(3 \pi t+\frac{\pi}{3}\right)\right]$
$=6 \sin \left(3 \pi t+\frac{\pi}{3}\right)$
ratio of their amplitude is $1 .$
Hence,
Option $A$ is correct answer.