Acccording to the question,

Total distance= 10 km+12 km =22 kms

Total time = $$\begin{gathered} =\left(\frac{10}{12}\right)+\left(\frac{12}{10}\right) \\ =\frac{100+144}{120} \\ =\frac{244}{120}\mathrm{hrs} \end{gathered}$$

Average speed

$$\begin{gathered} =\frac{{\displaystyle \left(\frac{22}{1}\right)}}{\left({\displaystyle \frac{244}{120}}\right)} \\ =\frac{22\times 120}{1\times 244}=\frac{11\times 120}{122} \\ =\frac{11+60}{61}=\frac{660}{61} \end{gathered}$$

= 10.8 kmph

Hence, Option B is correct.