A cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm ^{-1} K ^{-1}$ is welded end to end to copper rod of thermal conductivity $400 \,Wm ^{-1} K ^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ} C$ and that of the copper rod at $0^{\circ} C$. Assuming that the rods are perfectly insulated from the surrounding, the temperature at the junction of the two rods is ................... $^{\circ} C$
KVPY 2012, Medium
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