A body initially at 80^ C cools to 64^ C in 5 ~min and to 52^ C in...

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 $\quad 3.2=K$\left[72-\theta_0\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]$Dividing (i) by (ii), we get$\frac{3.2}{2.4}=\frac{72-\theta_0}{58-\theta_0}$or$\quad 185.6-3.2 \theta_0=172.8-2.4 \theta_0$or$\theta_0=16^{\circ} \mathrm{C}