Two liquids $\mathrm{A}$ $\mathrm{a}\mathrm{n}\mathrm{d}$ $\mathrm{B}$ form an ideal solution. At $300$ $\mathrm{K}$ the vapour pressure of a solution of $1$ $\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}$ of $\mathrm{A}$ and $\mathrm{x}$ moles of $\mathrm{B}$ is $550$ $\mathrm{m}\mathrm{m}$ of Hg. If the vapour pressures of pure $\mathrm{A}$ $\mathrm{a}\mathrm{n}\mathrm{d}$ $\mathrm{B}$ are $400$ $\mathrm{m}\mathrm{m}$ of Hg nd $600$ $\mathrm{m}\mathrm{m}$ of Hg respectively, then $\mathrm{x}$ is -