According to Newton’s law of cooling, the rate of loss of heat $∝$cooling difference in temperature. Here, average of 80°C and 50°C = 65°CTemperature of surroundings = 20°C∴ Difference = 65 – 20 = 45°CUnder these conditions, the body cools 30°C in 5 minutes.$\frac{\text{Change in temp.}}{\text{Time}} = k \Delta T$or ${30}/{5}=k × 45°{C}...(i)$The average of 60°C and 30° is 45°C which is 25°C (45 – 20) above the room temperature and the body cools by 30°C (60 – 30) in a time t (say).$\therefore\frac{30}{t}=k\times 25^\circ\mathrm{C}\dots\text{(ii)}$where k is same for this situation as for the original.Divide (i) by (ii)$\ {30 / 5}/{30 / t}= {k ×45}/{k ×25}$ or ${t}/{5}= {9}/{5}$$t=9 {min}$