$\begin{array}{1 1}400mm,600mm\\200mm,400mm\\500mm,200mm\\300mm,800mm\end{array} $

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Since $P=x_AP_A^0+x_BP_B^0$

$\Rightarrow \big(\large\frac{1}{1+3}\big)$$P_A^0+\big(\large\frac{3}{1+3}\big)$$P_B^{\large\circ}$=550mm Hg

$\Rightarrow \big(\large\frac{1}{1+4}\big)$$P_A^0+\big(\large\frac{4}{1+4}\big)$$P_B^{\large\circ}$=560mm Hg

That is,

$0.25P_A^0+0.75P_B^0$=550mm Hg

$0.20P_A^0+0.8P_B^0$=560mm Hg

Solving for $P_A^0$ and $P_B^0$ we get,

$P_A^0=400$ mm Hg

$P_B^0=600$ mm Hg

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