According to Newton’s law of cooling
$\frac{\theta_{1}-\theta_{2}}{t}=K\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right]$
In the first case, $\frac{80-64}{5}=K\left[\frac{80+64}{2}-\theta_{0}\right]$
or$\quad3.2=\,K\,\left[58-\theta_{0}\right]\quad\quad\quad\quad\quad\quad....\left(i\right)$
In the second case,$\, \frac{64-52}{5}=K\left[\frac{64+52}{2}-\theta_{0}\right]$
or$\quad 2.4 = K \left[58 - \theta_{0}\right]\quad \quad \quad \quad \quad \quad ....\left(ii\right)$
Dividing (i) by (ii), we get $\frac{3.2}{2.4}=\frac{72-\theta_{0}}{58-\theta_{0}}$
or $\quad185.6 - 3.2\theta_{0} = 172.8 - 2.4\theta _{0} \,\,$or $\,\,\theta _{0} = 16^{\circ}C$