Certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54 °C in the next 5 minutes. The temperature of the surroundings is:

By newton's law of cooling
$\frac{{\mathrm{\theta }}_1-{\mathrm{\theta }}_2}{\mathrm{t}}=\mathrm{k}\left[\frac{{\mathrm{\theta }}_1+{\mathrm{\theta }}_2}{2}-{\mathrm{\theta }}_0\right]$

$\Rightarrow \frac{70-60}{5}=\mathrm{k}\left[\frac{70+60}{2}-{\mathrm{\theta }}_0\right]$

$\Rightarrow 2=\mathrm{k}\left[65-{\mathrm{\theta }}_0\right] ..\left(\mathrm{i}\right)$

$\mathrm{and}, \frac{60-54}{5}=\mathrm{k} \left[\frac{60+54}{2}-{\mathrm{\theta }}_0\right]$

$\Rightarrow \frac{6}{5}=\mathrm{k}\left[57-{\mathrm{\theta }}_0\right] ..\left(\mathrm{ii}\right)$
By dividing eqn.(i) by eqn.(ii) we have 
$\frac{10}{6}=\frac{65-{\mathrm{\theta }}_0}{57-{\mathrm{\theta }}_0}\Rightarrow {\mathrm{\theta }}_0={45}^{\mathrm{o}}$