Let junction temperature is $T^{\circ} C$.

Then, assuming no heat loss and steady state,

Heat flow through copper rod per second $=$ Heat flow through steel rod per second

$\Rightarrow \frac{K_{\text {Copper }} A(100-T)}{l}=\frac{K_{\text {steel }} A(T-0)}{l}$

$\Rightarrow \quad K_{\text {Copper }}(100-T)=K_{\text {steel }} \cdot T$

$\therefore$ Area and length of both rods are equal.

$\therefore$ Area and length of both rods are equal.

Substituting values, we get

$385(100-T)=50 \,T$

$\Rightarrow \quad 385 \times 100=(385+50) \,T$

$\Rightarrow \quad T=\frac{385 \times 100}{435} \approx 88^{\circ} C$