A mixture of $O_2$ and gas $Y$ (molecular weight $=80$) in the molar ratio $a:b$ has a mean molecular weight $40$. What would be mean molecular weight, if the gases are mixed in the ratio $b:a$ under identical conditions? (Gases are non-reacting)

The correct option is D $72$
Let mole fraction of $O_2$ is $x$.
The mean molecular weight of the mixture is $40$.
$\Rightarrow 40=32\times x+80\times (1-x)\Rightarrow x=\frac{5}{6}$
$\therefore a:b=x:(1-x)=\frac{5}{6}:\frac{1}{6}$
When the ratio is changed to $\frac{1}{6}:\frac{5}{6}$, then the mean molecular weight of the mixture is
$=32\times \frac{1}{6}+80\times \frac{5}{6}=72$