Let stone is projected with initial velocity $v$.

Kinetic energy of the stone at point of projection is $K{E}_1=\frac{1}{2}m{v}^2$.

Now, velocity of stone at maximum height is $=v\cos 30°$, so kinetic energy at that point is $K{E}_2=\frac{1}{2}m{\left(v\cos 30°\right)}^2$

Hence, the ratio $\frac{K{E}_1}{K{E}_2}=\frac{{\displaystyle \frac{1}{2}m{v}^2}}{{\displaystyle \frac{1}{2}m{\left(v\cos 30°\right)}^2}}=\frac{4}{3}$