Two vessels A and B are of the same size and are at same...

For both the gases, it follows that

$\dfrac{{P}_{A}{V}_{A}}{{P}_{B}{V}_{B}} = \dfrac{{n}_{A}R{T}_{A}}{{n}_{B}R{T}_{B}} . . . \left(1\right)$

Given ${V}_{A} = {V}_{B}$ and ${T}_{A} = {T}_{B}$.

Thus, from equation (1), it follows that

$\begin{cases}\dfrac{{P}_{A}}{{P}_{B}} & = & \dfrac{{n}_{A}}{{n}_{B}} \\ & = & \dfrac{\dfrac{1}{2}}{\dfrac{1}{32}} \\ & = & 16\end{cases}$