$Density =( mass ) /( Volume )$

i.e. $\rho=( M / V )$

$\therefore P \times( M / \rho)= nRT$

$\therefore P =\{( nRT \rho) / M \}$

$( P / \rho T )=\text { constant }$

Given: pressure is doubled, Temper attire is $4$ times.

As $\left(P_{2} / P_{1}\right)=\left\{\left(\rho_{2} T_{2}\right) /\left(\rho_{1} T_{1}\right)\right\}$

$\therefore\left\{2 P _{1} / P _{1}\right\}=\left(\rho_{2} / \rho_{1}\right) \cdot\left\{4 T _{1} / T _{1}\right\}$

$\therefore\left(\rho_{1} / \rho_{1}\right)=(1 / 2)$

$\therefore \rho_{2}=\left(\rho_{1} / 2\right)$

Hence density is halved.