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 $55 \ kNm^{-2}$ and $15 \ kNm^{-2}$ respectively. What is the mole fraction of $A$ in the solution of $A$ and $B$ in equilibrium with a vapour in which the mole fraction of $A$ is $0.8$?

• A
  $0.5217$
• B
  $0.480$
• C
  $0.663$
• D
  $0.340$