Physics Question from JEE Main 2023 · 13 April, Shift 2

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 the same surface area and the 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 _____ $^\circ \text{C}$.