A body cools from $$80°$$C to $$60°$$ in $$5$$ minutes. The temperature for the surrounding is $$20°$$C. The time it takes to cool from $$60°$$C to $$40°$$C is

$$\frac{\theta_1 - \theta_2}{t} = K \left( \frac{\theta_1 + \theta_2}{2} - \theta_s \right)$$

Case 1: Cooling from $$80^\circ\text{C}$$ to $$60^\circ\text{C}$$

$$\frac{80 - 60}{300} = K \left( \frac{80 + 60}{2} - 20 \right)$$

$$\frac{20}{300} = K (70 - 20)$$

$$\frac{1}{15} = K(50) \implies K = \frac{1}{750}\text{ s}^{-1}$$

Case 2: Cooling from $$60^\circ\text{C}$$ to $$40^\circ\text{C}$$

$$\frac{60 - 40}{t_2} = \frac{1}{750} \left( \frac{60 + 40}{2} - 20 \right)$$

$$\frac{20}{t_2} = \frac{1}{750} (50 - 20)$$

$$\frac{20}{t_2} = \frac{1}{750} (30)$$

$$t_2 = 20 \times 25 = 500\text{ s}$$