Explanation

(b) From Newton’s law of cooling when a hot body is cooled in air, the rate of loss of heat by the body is proportional to the temperature difference between the body and its surroundings.
Given, $\theta_{1} = 60℃,\ \ \ \theta_{2} = 50℃,\ \ \ \ \theta = 25℃$
$\therefore$ Rate of loss of heat=K
(Mean temp.-Atmosphere temp.)
Where K is coefficient of thermal conductivity
$\frac{\theta_{1} - \theta_{2}}{t} = K\left( \frac{\theta_{1} + \theta_{2}}{2} - \theta \right)$
$\frac{60 - 50}{10} = K\left( \frac{60 + 50}{2} - 25 \right)$
$\Rightarrow$ $K = \frac{1}{30}$
Also putting the value of $K$, we have
$\frac{50 - \theta_{3}}{10} = \frac{1}{30}\left( \frac{50 + \theta_{3}}{2} - 25 \right)$
$\Rightarrow$ $\theta_{3} = 42.85℃$