At 300K , the vapour pressure of a solution containing 1 mole of n...

${P}_{total} = {P}^{∘}hexane . {X}_{hexane} + {P}^{∘}heptane . {X}_{heptane}$

$550 = \left[{P}^{∘}hexane\right] \times \dfrac{1}{4} + \left[{P}^{∘}heptane\right] \times \dfrac{3}{4}$ ..$( i )$

After mixing $1$ mole n-heptane

$560 = \left[{P}^{∘}hexane\right] \times \dfrac{1}{5} + \left[{P}^{∘}heptane\right] \times \dfrac{4}{5}$ .....$( ii )$

On solving eq. (i) and (ii)

${P}^{∘}heptane = 600mm$ of $Hg$