An object of mass 5   kg is thrown vertically upwards from the ground. The air resistance produces a…

Net force while going upward will be $mg+R=50+10=60 \mathrm{N}$

$\Rightarrow a_{up}=\frac{60}{5}=12 \mathrm{m} {\mathrm{s}}^{-2}$

Similarly, Net force while going downward will be $mg-R=40 \mathrm{N}$

$\Rightarrow a_d=\frac{40}{5}=8 \mathrm{m} {\mathrm{s}}^{-2}$

Since 

$$\begin{gathered} h=\frac{1}{2}a{t}^2 \\ \Rightarrow \frac{a_{up}{t_{up}}^2}{a_d{t_d}^2}=1\Rightarrow \frac{t_{up}}{t_d}=\sqrt{\frac{8}{12}}=\sqrt{\frac{2}{3}} \end{gathered}$$