Three rods of the same length and cross-section are joined at one end to a common junction J, as shown in the figure. Their thermal conductivities are $K$, $2K$ and $3K$. The free ends of these rods are held at $0\ ^\circ\text{C}$, $50\ ^\circ\text{C}$ and $100\ ^\circ\text{C}$ respectively. The sides of the rods are insulated. In the steady state, what is the temperature of the junction?

Fig. 1: Three rods of equal length joined at a junction J. Their thermal conductivities are K, 2K and 3K, and their free ends are held at 0, 50 and 100 degrees Celsius respectively.