a
$B =- V \frac{ dP }{ dV }$
Thus, $\Delta V =-\frac{ pV }{ B }$ or $V ^{\prime}- V =-\frac{ pV }{ B }$ Or, $V^{\prime}=V\left(1-\frac{p}{B}\right)$
Now, $\rho^{\prime}=\frac{ m }{ V ^{\prime}}=\frac{ m }{ V \left(1-\frac{ P }{ B }\right)}=\frac{\rho}{\left(1-\frac{ p }{ B }\right)}$
$\frac{\rho^{\prime}}{\rho}=\frac{1}{\left(1-\frac{ p }{ B }\right)}$