When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity…

Maximum kinetic energy is expressed as $K_{\max }=hf-\varphi$, here, $\varphi$ is work function of metal.

For first case, $\frac{1}{2}{m{v}_1}^2=h\left[\left(2f_0\right)-f_0\right]$

For second case, $\frac{1}{2}{m{v}_2}^2=h\left[\left(5f_0\right)-f_0\right]$

$\Rightarrow \frac{{v_2}^2}{{v_1}^2}=\frac{4}{1}\Rightarrow \frac{v_2}{v_1}=2$