If 0.03 × 0.3a = 0 .3 × 0 .3 × b , value of a/b\, is?

Answer: Option C

$$\begin{array}{rl}& \sqrt{0.03\times 0.3a}=\text{0}\text{.3}\times \text{0}\text{.3}\times \sqrt{b}\\ & \text{Squaring both sides}\\ & \Rightarrow \text{0}\text{.03}\times \text{0}\text{.3a}={\left(0.3\right)}^2\times {\left(0.3\right)}^2\times b\\ & \Rightarrow \frac{3}{100}\times \frac{3}{10}a=\frac{9}{100}\times \frac{9}{100}\times b\\ & \Rightarrow 9a=\frac{81}{10}b\\ & \Rightarrow 90a=81b\\ & \Rightarrow 10a=9b\\ & \Rightarrow \frac{a}{b}=\frac{9}{10}\\ & \Rightarrow \frac{a}{b}=0.9\end{array}$$