According to the approximate form of Newton's law of cooling: $\frac{\Delta T}{\Delta t} = K \left( \frac{T_1 + T_2}{2} - T_s \right)$ Where $T_s = 25^\circ \text{C}$ is the surrounding temperature.

Case 1: Cooling from $80^\circ \text{C}$ to $70^\circ \text{C}$ in $12 \text{ min}$ $\frac{80 - 70}{12} = K \left( \frac{80 + 70}{2} - 25 \right)$ $\frac{10}{12} = K (75 - 25)$ $\frac{10}{12} = K (50)$ $\implies K = \frac{1}{60} \text{ min}^{-1}$

Case 2: Cooling from $70^\circ \text{C}$ to $60^\circ \text{C}$ in $t \text{ min}$ $\frac{70 - 60}{t} = K \left( \frac{70 + 60}{2} - 25 \right)$ $\frac{10}{t} = K (65 - 25)$ $\frac{10}{t} = K (40)$

Substituting the value of $K$ from Case 1: $\frac{10}{t} = \frac{1}{60} \times 40$ $\frac{10}{t} = \frac{2}{3}$ $\implies t = \frac{30}{2} = 15 \text{ min}$.