$\rho=\frac{m}{n e^{2} \tau}$

where, $m$ is mass of an electron, $e$ is charge on electron, $n$ is number of free electrons per unit volume in conductor and $\tau$ is relaxation time.

$\Rightarrow \rho \propto \frac{1}{\tau}$$.............(1)$

Also, the conductivity is reciprocal of resistivity i.e.

$\sigma=\frac{1}{\rho}$$...............(2)$

$\Rightarrow \sigma \propto \tau$$............(3)……….$ from $(1)$ and $(2)$

$\frac{\rho}{\sigma} \propto \frac{1}{\tau^{2}} ........$ from $(1)$ and $(3)$

When temperature increases relaxation time will decrease and hence, ratio of resistivity and conductivity will increase.