A gun fires two bullets at ${60}^{\circ }$ and ${30}^{\circ }$ with the horizontal at same speed. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio:

The correct option is C $3:1$
As we know, the maximum height attained by the particle $h=\frac{u^2{\sin }^2\theta }{2g}$

Given that, the bullets are fired at the same initial speed.

$\frac{h}{h^{\prime }}=\frac{u^2{\sin }^2{60}^{\circ }}{2g}\times \frac{2g}{u^2{\sin }^2{30}^{\circ }}$

$\frac{h}{h^{\prime }}=\frac{{\sin }^2{60}^{\circ }}{{\sin }^2{30}^{\circ }}=\frac{3}{1}$

Hence, option $\left(\text{B}\right)$ is correct.