Given, $\left(\mathrm{H}_{\max }\right)_1=8 \times\left(\mathrm{H}_{\max }\right)_2$ $$ \begin{aligned} & \frac{\mathrm{u}^2 \sin ^2 \theta_1}{2 \mathrm{~g}}=8 \times \frac{\mathrm{u}^2 \sin ^2 \theta_2}{2 \mathrm{~g}} \\ & \Rightarrow \sin \theta_1=2 \sqrt{2} \sin \theta_2 \\ & \frac{\mathrm{~T}_1}{\mathrm{~T}_2}=\frac{2 \mathrm{u} \sin \theta_1 / \mathrm{g}}{2 \mathrm{u} \sin \theta_2 / \mathrm{g}}=\frac{\sin \theta_1}{\sin \theta_2}=2 \sqrt{2} \end{aligned} $$