Liquid M and liquid N form an ideal solution. The vapour pressures...

${P}_{M}^{o}$ is given as$= 450mmofHg .$

${P}_{N}^{o}$ is given as$= 700mmofHg .$

We know that ${P}_{M} = {x}_{M} \times {P}_{M}^{O} \to$ Raoult’s law.

${P}_{N} = {x}_{N} \times {P}_{N}^{O} \to$ Raoult’s law.

From Dalton’s law ${P}_{M} = {y}_{M} \times {P}_{T}$

${P}_{N} = {y}_{M} \times {P}_{T}$

So,

${x}_{M} \times {P}_{M}^{o} = {y}_{M} \times {P}_{T} \ldots ( i )$

${x}_{M} \times {P}_{N}^{o} = {y}_{N} \times {P}_{T} \ldots ( ii )$

$\dfrac{( i )}{( ii )}\dfrac{{x}_{M}}{{x}_{N}} \times {P}_{M}^{o}{P}_{N}^{o}=\dfrac{{y}_{M}}{{y}_{N}}$

$\dfrac{{x}_{M}}{{x}_{N}} = \dfrac{{y}_{M}}{{y}_{N}} \times \dfrac{750}{450}$

$\dfrac{{x}_{M}}{{x}_{N}} > \dfrac{{y}_{M}}{{y}_{N}}$