For an ideal solution \(P_S = P _{A} ^{\circ} X_A + P_B ^{\circ} X_B\)
\(X_A = \frac{1}{4}\)
\(X_B = \frac{3}{4}\)
\(500 = 200 \times \frac{1}{4} + P _{B}^{\circ} \times \frac{3}{4}\)
\(P_B^{\circ} \times \frac{3}{4} = 450\)
\(P_{B}^{\circ} = \frac{450 \times 4}{3} = 600\ mm Hg\)