$\text{Charge in the capacitor at time t } q= q_0 e^{\frac{-t}{RC}}$

$\Rightarrow q = q_0 e^{\frac{-t_2}{RC}} = \frac{q_0}{4}$

$ \Rightarrow \frac{t_2}{RC} = ln4=2ln2 $

$\Rightarrow t_2 = 2ln2 RC$

$U = \frac{U_i}{2}$

$\Rightarrow \frac{1}{2}\frac{q_0^2}{2C} = \frac{q_0^2}{2C} e^{\frac{-2t_1}{RC}}$

$ e^{\frac{-2t_1}{RC}} = \frac{1}{2}$

$\frac{2t_1}{RC} = ln2$

$\Rightarrow t_1 = \frac{ln2}{2} RC$

$\frac{t_1}{t_2} = \frac{1}{4}$