Question : If $\sqrt{0.04\times 0.4\times a}=0.004\times 0.4\times \sqrt{b},$ then the value of $\frac{a}{b}$ is:
Option 1: $16\times 10^{-3}$
Option 2: $16\times 10^{-4}$
Option 3: $16\times 10^{-5}$
Option 4: $16 \times 10^{-6}$
Correct Answer: $16\times 10^{-5}$
Solution :
$\sqrt{0.04\times 0.4\times a}=0.004\times 0.4\times \sqrt{b}$
Squaring both sides, we get,
$⇒0.04\times 0.4\times a=0.004^2\times 0.4^2\times {b}$
$⇒\frac{a}{b} = \frac{0.004 \times 0.004 \times 0.4 \times \times0.4}{0.04 \times 0.4}$
$⇒\frac{a}{b} = \frac{16}{10^{5}}$
$\therefore$ $\frac{a}{b} = 16 \times 10^{-5}$
Hence, the correct answer is $16 \times 10^{-5}$.
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