At ${10}^0\mathrm{C}$ the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At 110"C this ratio is

Writing ideal gaw law, PV = nRT

or $\mathrm{PV} =\frac{ \mathrm{m}}{\mathrm{M}}\mathrm{RT} \mathrm{or} \frac{\mathrm{PV}}{\mathrm{m}} = \frac{1}{\mathrm{M}}\mathrm{RT}$

or $\frac{\mathrm{p}}{\mathrm{\rho }} = \frac{\mathrm{RT}}{\mathrm{M}} \mathrm{or} \frac{\mathrm{\rho }}{\mathrm{P}} = \frac{1}{\mathrm{T}}$

$\therefore \frac{{\displaystyle \frac{{\mathrm{\rho }}_1}{{\mathrm{P}}_1}}}{{\displaystyle \frac{{\mathrm{\rho }}_2}{{\mathrm{P}}_2} }} = \frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}$

$\Rightarrow \frac{\mathrm{x}}{\left({\displaystyle \frac{{\mathrm{\rho }}_2}{{\mathrm{P}}_2}}\right)} = \frac{383}{283} \mathrm{or} \frac{{\mathrm{\rho }}_2}{{\mathrm{P}}_2} = \frac{283}{383}\mathrm{x}$