At $300 \mathrm{~K}$, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is $550 \mathrm{~mm}$ of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by $10 \mathrm{~mm}$ of Hg. What is the vapour pressure in $\mathrm{mm} \mathrm{Hg}$ of n-heptane in its pure state_________ ?
$550=\mathrm{P}_{\mathrm{A}}^{\circ} \times \frac{1}{4}+\mathrm{P}_{\mathrm{B}}^{\circ} \times \frac{3}{4}$
$2200=\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}+3 \mathrm{P}_{\mathrm{B}}^{\mathrm{o}}$ $\ldots . .(\mathrm{i})$
$2800=\mathrm{P}_{\mathrm{A}}^{0}+4 \mathrm{P}_{\mathrm{B}}^{0}$ ....(ii)
$560=\mathrm{P}_{\mathrm{A}}^{0} \times \frac{1}{5}+\mathrm{P}_{\mathrm{B}}^{0} \times \frac{4}{5}$
$P_{B}^{\circ}=600, P_{A}^{\circ}=400$
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