Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperatures 200^oC and 20^oC, respectively. The temperature of junction B will be

Let the thermal resistance of each rod be R.
The two resistances connected along two paths from B to C are equivalent to 2R each and their parallel combination is R. Effective thermal resistance between B and D = 2R 

$\text{ Temperature of interface }\mathrm{\theta }=\frac{{\mathrm{R}}_1{\mathrm{\theta }}_2+{\mathrm{R}}_2{\mathrm{\theta }}_1}{{\mathrm{R}}_1+{\mathrm{R}}_2}$

$\mathrm{\theta }=\frac{\mathrm{R}\times 20+2\mathrm{R}\times 200}{\mathrm{R}+2\mathrm{R}}=\frac{420}{3}={140}^{\circ }\mathrm{C}$