From the top of a tower a body A is thrown up vertically with velocity u and another body B is thrown vertically down with the same velocity u. If v_A and v_B are their velocities when they reach the ground and t_A and t_B are their times of flight, then

Taking all upward physical quantities negative and downward physical quantities positive,

For stone A and stone B, ${\mathrm{v}}^2={\mathrm{u}}^2+2\mathrm{gh}$ and ${\mathrm{v}}^2={(-\mathrm{u})}^2+2\mathrm{gh}$ we can conclude that the final velocities will be equal.

Stone will reach a height above the tower and come back to the top of tower and will fall down to surface of earth, whereas the stone B will fall directly to surface of earth.

So ${\mathrm{t}}_{\mathrm{A}}>{\mathrm{t}}_{\mathrm{B}}$