At 600K , the root mean square ( rms ) speed of gas X (molar mass =...

The root mean square velocity ${V}_{rms} = \sqrt{\dfrac{3RT}{M}}$

The most probable speed ${V}_{mp} = \sqrt{\dfrac{2RT}{M}}$

$T =$Temperature in Kelvin

$M =$Molar mass

$\dfrac{{V}_{rms}of X}{{V}_{mp}of Y} = \sqrt{\dfrac{3{T}_{X}{M}_{Y}}{2{T}_{Y}{M}_{X}}}$

$1 = \sqrt{\dfrac{3 \times 600 \times {M}_{Y}}{2 \times 90 \times 40}} = \sqrt{\dfrac{{M}_{Y}}{4}}$

${M}_{Y} = 4gm{mol}^{- 1}$