The Total pressure observed by mixing two liquid AandB is 350mmHg...

Let Vapour pressure of pure $A$ be ${P}_{A}^{o}$

Let Vapour pressure of pure $B$ be ${P}_{B}^{o}$

Using Raoult's law and Dalton's law:

When{X}_{A} = 0 . 7 \text{ and } {X}_{B} = 0 . 3{P}_{s} = 350 ⇒ {P}_{A}^{o} \times 0 . 7 + {P}_{B}^{o} \times 0 . 3 = 350 . . . . ( i ) When{X}_{A} = 0 . 2 \text{ and } {X}_{B} = 0 . 8{P}_{s} = 410 ⇒ {P}_{A}^{o} \times 0 . 7 + {P}_{B}^{o} \times 0 . 3 = 350 . . . . ( ii ) Solving ( i ) and ( ii ) {P}_{A}^{o} = 314mmHg{P}_{B}^{o} = 434mmHg$