If 310 × 272 = 92 × 3n then the value of n is = ?

Answer: Option B

$$\begin{array}{rl}& {\text{3}}^{10}\times \text{2}{\text{7}}^2\text{ = }{\text{9}}^2\times {\text{3}}^n\\ & \Rightarrow {\text{3}}^{10}\times {\left(3^3\right)}^2\text{ = }{\left(3^2\right)}^2\times {\text{3}}^n\\ & \Rightarrow {\text{3}}^{10+6}\text{ = }{\text{3}}^{4+n}\\ & \Rightarrow 10+6=4+n\\ & \Rightarrow n=12\end{array}$$