Question

A solution of methanol and water has a vapour pressure of 213 Torr. What would you predict as the mole fractions of each component, assuming ideal behaviour? The vapour pressures of methanol and water are 256 Torr and 55.3 Torr, respectively

Answer 1

Difference in p of solvents = 256-55.3 = 200.7

(256-213)/200.7 = about 0.2
(213-55.3)/200.7 = about 0.8

So the 0.2 is closer to the Xmethanol.
The 0.8 must be XH2O

Answer 2

By the way those are estimates. You should recalculate to get more exact numbers.