Two liquids $A$ and $B$ form an ideal solution at temperature $T K$. At $T K$, the vapour pressures of pure $A$ and $B$ are 55 and $15 \mathrm{kNm}^{-2}$ respectively. What is the mole fraction of $A$ in solution of $A$ and $B$ in equilibrium with a vapour in which the mole fraction of $A$ is $0.8 ?$