If 0.04 × 0.4 × a = 0.004 × 0.4 × b , then the value of a/b\, is?

Answer: Option C

$$\begin{array}{rl}& \sqrt{0.04\times 0.4\times a}=0.004\times 0.4\times \sqrt{b}\\ & \Rightarrow \sqrt{\frac{4}{100}\times \frac{4}{10}\times a}=\frac{4}{1000}\times \frac{4}{10}\times \sqrt{b}\\ & \Rightarrow \frac{4}{10}\sqrt{\frac{a}{10}}=\frac{4}{10}\times \frac{4}{1000}\times \sqrt{b}\\ & \Rightarrow \frac{a}{10}=\frac{16}{1000000}\times b\\ & \Rightarrow \frac{a}{b}=\frac{16\times 10}{1000000}\\ & \Rightarrow \frac{a}{b}=\frac{16}{100000}\\ & \Rightarrow \frac{a}{b}=16\times 10^{-5}\end{array}$$