At steady state, the temperature at different parts of the solid remains constant and is independent of time. Therefore, the ratio of the difference in temperature to the distance between two points in a heated body under a steady state is called the temperature gradient will be constant.

Let a point $C$between the ends of rod which is $9 \mathrm{cm}$from $A,$since temperature gradient is constant in the given thermal conduction process.

$$\begin{gathered} \frac{T_A-T_C}{9}=\frac{T_A-T_B}{20} \\ \Rightarrow \frac{100-T_C}{9}=\frac{100-0}{20} \\ \Rightarrow T_C=100-\frac{900}{20}=55°\mathrm{C} \end{gathered}$$