$Q = \frac{KA(\Delta \theta) t}{l}$ $\therefore$ Q and $\Delta \theta$ are same for both spheres hence $K \propto \frac{1}{At} \propto \frac{1}{r^2 t} \Rightarrow \frac{k_{\text{larger}}}{k_{\text{smaller}}} = \frac{l_1}{l_s} \times \left(\frac{r_s}{r_1}\right)^2 \times \frac{t_s}{t_1}$. It is given that $r_1 = 2r_s$, $l_1 = \frac{1}{4} l_s$ and $t_1 = 25 \text{ min}$, $t_s = 16 \text{ min}$. $\Rightarrow \frac{k_{\text{larger}}}{k_{\text{smaller}}} = \left(\frac{1}{4}\right) \left(\frac{1}{2}\right)^2 \times \frac{16}{25} = \frac{1}{25}$