Two liquids $X$ and $Y$ form an ideal solution. At a constant temperature of $300 \ K$,the vapor pressure of a solution containing $1 \ mol$ of $X$ and $3 \ mol$ of $Y$ is $550 \ mm \ Hg$. If $1 \ mol$ of $Y$ is added to this solution,the vapor pressure of the solution increases by $10 \ mm \ Hg$. What are the vapor pressures of $X$ and $Y$ in their pure states?

• A
  $400 \ mm \ Hg$ and $600 \ mm \ Hg$
• B
  $500 \ mm \ Hg$ and $600 \ mm \ Hg$
• C
  $200 \ mm \ Hg$ and $300 \ mm \ Hg$
• D
  $300 \ mm \ Hg$ and $400 \ mm \ Hg$