\(Density =( mass ) ( Volume )\)

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.