The thermal conductivity of a material determines how well it can conduct heat. In this question, it is stated that the thermal conductivity of copper is 4 times that of brass.

When two rods of copper and brass are joined end to end, heat will flow from the hot end (100°C) of the brass rod to the cold end (0°C) of the copper rod.

Since copper has a higher thermal conductivity than brass, it means that copper can conduct heat more effectively. Therefore, heat will flow more rapidly through the copper rod than through the brass rod.

As a result, the temperature at the junction between the two rods will be lower than the initial temperature of the brass rod but higher than the initial temperature of the copper rod.

Based on this information, we can conclude that the correct answer is option 1: 20°C. This is because the temperature at the junction will be a balance between the heat transfer from the brass rod and the heat transfer to the copper rod.