An ideal solution has two component A and B. A is more volatile than B and also ${\mathrm{P}}_{\mathrm{A}}^0>{\mathrm{P}}_{\mathrm{total} }$. If X_A and Y_A are the mole fractions of A in the liquid and vapour phase then

According to Raoult's law, the partial pressure of a component of solution is equal to its mole fraction in the solution multiplied by its vapour pressure in pure state.

${\mathrm{P}}_{\mathrm{A}}={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}} ......\left(1\right)$

According to Dalton law of partial pressures, the partial pressure of a component of a gas is equal to the product of the total pressure and mole fraction of the gas in gaseous state.

${\mathrm{P}}_{\mathrm{A}}={\mathrm{P}}_{\mathrm{T}}{\mathrm{Y}}_{\mathrm{A}} .....\left(2\right)$

Combining equations (1) and (2) we get, 

$$\begin{gathered} {\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}={\mathrm{P}}_{\mathrm{T}}{\mathrm{Y}}_{\mathrm{A}} \\ \mathrm{But} {\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}>{\mathrm{P}}_{\mathrm{T}} \\ \mathrm{Hence}, {\mathrm{X}}_{\mathrm{A}}<{\mathrm{Y}}_{\mathrm{A}} \end{gathered}$$