Two materials having coefficients of thermal conductivity $3\mathrm{K}$ and $\mathrm{K}$ and thickness $\mathrm{d}$ and $3\text{d}$ respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are ${\mathrm{\theta }}_2$ and ${\mathrm{\theta }}_1$ respectively, $\left({\mathrm{\theta }}_2>{\mathrm{\theta }}_1\right).$ The temperature at the interface is

• A

  $\frac{{\mathrm{\theta }}_2+{\mathrm{\theta }}_1}{2}$
• B

  $\frac{{\mathrm{\theta }}_1}{6}+\frac{5{\mathrm{\theta }}_2}{6}$
• C

  $\frac{{\mathrm{\theta }}_1}{3}+\frac{2{\mathrm{\theta }}_2}{3}$
• Correct answer
  D

  $\frac{{\mathrm{\theta }}_1}{10}+\frac{9{\mathrm{\theta }}_2}{10}$

Hence, the correct answer is option: 'D'.