The molecules of a given mass of gas have RMS velocity of 200 m s - 1 at 27 o C and 1.0 × 10 5 N m - 2…

RMS speed of molecules is $V_{\mathrm{RMS}}=\sqrt{\frac{3RT}{M}}$, where $R$ is universal gas constant, $T$ is absolute temperature and $M$ is molar mass of gas.
So it depends only on temperature, $V_{\mathrm{r}\mathrm{m}\mathrm{s}}\propto \sqrt{T}$
$\Rightarrow \frac{V_1}{V_2}=\sqrt{\frac{T_1}{T_2}}\Rightarrow \frac{200}{V_2}=\sqrt{\frac{300}{400}}$
$\Rightarrow \frac{200}{V_2}=\frac{\sqrt{3}}{2}\Rightarrow V_2=\frac{400}{\sqrt{3}} \mathrm{m} {\sec }^{-1}$