The rates of diffusion of two gases $\ce{A}$ and $\ce{B}$ are in the ratio $1:4$. If the ratio of their masses present in the mixture is $2:3$, the ratio of their mole fraction is?
My tries:
$\frac{r_1}{r_2}=\frac{1}{4}=\sqrt{\frac{M_2}{M_1}}\to\frac{1}{16}=\frac{M_2}{M_1}$, $M_i$ is molar mass of $i$.
Also given $\frac{w_1}{w_2}=\frac{2}{3}$, multiplying this by above one gives $\frac{M_2\cdot w_1}{M_1\cdot w_2}=\frac{2}{3\cdot 16}\to\frac{n_1}{n_2}=\frac{1}{24}$, where $n_i$ represents number of moles of $i$.
But this is not a correct answer please help.