1. Heat current in steady state

For two rods connected in series, in steady state the heat current through both rods is same:

Here:

• steel rod parameters: $K_1, A_1, L_1$
• copper rod parameters: $K_2, A_2, L_2$
• junction temperature: $T$

From the figure, the end temperatures are $90^\circ\mathrm{C}$ and $0^\circ\mathrm{C}$, so:

2. Use the given ratios

Given:

We need the ratio:

Now,

Substitute values:

So,

Thus the steady-state equation becomes:

Cancelling common factor:

3. Check with options

The computed value $9^\circ\mathrm{C}$ is not present in the listed options. This indicates that the figure likely has different endpoint temperatures than those inferable from the text alone.

For the stored answer $45^\circ\mathrm{C}$ to be correct, the two rods would need equal thermal resistance, but from the given ratios:

and

So the steel rod has $9$ times the thermal resistance of the copper rod, hence the temperature drop across steel should be $9$ times that across copper. Therefore the junction temperature must lie much closer to the cold end, not at $45^\circ\mathrm{C}$.

Thus, using the given ratios, the stored answer cannot be justified unless the figure contains additional temperature values not included in the text.