Thermal Properties of Matter question for JEE Main (JEE Main 2023 (13 Apr, Shift 2)), with solution

Two plates A and B have thermal conductivities $84\ \text{W m}^{-1}\text{K}^{-1}$ and $126\ \text{W m}^{-1}\text{K}^{-1}$ 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 $100^\circ\text{C}$ and $0^\circ\text{C}$ respectively, then the temperature of the surface of contact in steady state is ______ $^\circ\text{C}$.