Two plates A and B have thermal conductivities $84 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$ and $126 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of  A and B are kept at ${100}^{\circ }\mathrm{C}$ and $0^{\circ }\mathrm{C}$ respectively, then the temperature of the surface of contact in steady state is_____ ${}^{\circ }\mathrm{C}$.

Hence, the correct answer is 40.