Chemistry Question from JEE Main 2023 · 24 January, Shift 2

The total pressure observed by mixing two liquids $A$ and $B$ is $350 \, \text{mm Hg}$ when their mole fractions are $0.7$ and $0.3$ respectively. The total pressure becomes $410 \, \text{mm Hg}$ if the mole fractions are changed to $0.2$ and $0.8$ respectively for $A$ and $B$. The vapour pressure of pure $A$ is ______ mm Hg. (Nearest integer)

Consider the liquids and the solution to behave ideally.__