The molecules of a given mass of gas have RMS velocity of 200 m s ^...

RMS speed of molecules is ${V}_{RMS} = \sqrt{\dfrac{3RT}{M}}$, where $R$ is universal gas constant, $T$ is absolute temperature and $M$ is molar mass of gas.

So it depends only on temperature, ${V}_{rms} ∝ \sqrt{T}$

$⇒ \dfrac{{V}_{1}}{{V}_{2}} = \sqrt{\dfrac{{T}_{1}}{{T}_{2}}} ⇒ \dfrac{200}{{V}_{2}} = \sqrt{\dfrac{300}{400}}$

$⇒ \dfrac{200}{{V}_{2}} = \dfrac{\sqrt{3}}{2} ⇒ {V}_{2} = \dfrac{400}{\sqrt{3}}m{sec}^{- 1}$