According to the question

${\mathrm{n}}_1=30, {\mathrm{n}}_2=60, {\mathrm{a}}_1=12, {\mathrm{a}}_2=10$

We know the formula,

Weighted average(Aw)$=\frac{{\mathrm{n}}_1{\mathrm{a}}_1+{\mathrm{n}}_2{\mathrm{a}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}$

Average age of the whole class

$$\begin{gathered} =\frac{30\times 12+60\times 10}{30+60} \\ =\frac{360+600}{90} \\ =\frac{960}{90} \end{gathered}$$

= 10.66 yr

Hence, Option B is correct.