A stone is thrown vertically up from the top of a tower with some initial velocity and it arrives on the ground after $t_1$ seconds. Now if the same the stone is thrown vertically down from the top of the same tower with the same initial velocity, it arrives on ground after $t_2$ seconds. In how much time will the stone take to reach the ground if it is dropped from the same tower?

Question

$\begin{array}{1 1}(A)\;\frac{t_1+t_2}{2} \\(B)\;\frac{t_1-t_2}{2}\\(C)\;t_1+t_2\\(D)\;\sqrt {t_1t_2} \end{array} $