PV = nRT

$\Rightarrow PV = {m \over M}RT$

$\Rightarrow {{PV} \over m} = {{RT} \over M}$

$\Rightarrow {P \over \rho } = {{RT} \over M}$

$\Rightarrow {P \over \rho } \propto T$

$\therefore {P \over \rho } \propto {1 \over T}$

${{{{{P_1}} \over {{\rho _1}}}} \over {{{{P_2}} \over {{\rho _2}}}}} = {{{T_1}} \over {{T_2}}} = {{383} \over {283}}$

$\Rightarrow {x \over {{{{P_2}} \over {{P_2}}}}} = {{383} \over {283}}$

$\therefore {{{P_2}} \over {{P_2}}} = {{383} \over {283}}x$