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 $\_\_\_\_$ ${ } ^ { \circ } \mathrm { C }$.
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 $\_\_\_\_$ ${ } ^ { \circ } \mathrm { C }$.