balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height  h. The time taken by the stone to reach the ground is

The velocity of balloon at height h, $v=\sqrt{2\left(\frac{g}{8}\right)h}$

When the stone is released from this balloon, it will go upward with velocity $v=\frac{\sqrt{gh}}{2}$ (same as that of balloon). In this condition, time taken by stone to reach the ground is

$\begin{array}{l}t=\frac{v}{g}\left[1+\sqrt{1+\frac{2gh}{v^2}}\right]\\ =\frac{\sqrt{gh}/2}{g}\left[1+\sqrt{1+\frac{2gh}{gh/4}}\right]=\frac{2\sqrt{gh}}{g}=2\sqrt{\frac{h}{g}}\end{array}$