Two vessels of different materials are identical in size and wall-thickness. They are filled with equal quantities of ice at $0^{0}C$ If the ice melts completely, in 10 and 25 minutes respectively then compare the coefficients of thermal conductivity of the materials of the vessels

Let $K_1$ and $K_2$ be the coefficient of thermal conductivity of the materials, and $t_1$ and  $t_2$ be the time in which ice melts in the two vessels. Since both the vessels are identical, so A and x in both the cases are same. Now,

  $Q=\frac{K_{1}A\left({\theta }_1-{\theta }_2\right)t_1}{L}=\frac{K_{2}A\left({\theta }_1-{\theta }_2\right)t_2}{L}$ $\Rightarrow \frac{K_1}{K_2}=\frac{t_2}{t_1}=\frac{25\text{\hspace{0.33em}}\min }{10\min }=\frac{5}{2}=2.5$