Question

If $\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$, the value of $\frac{b}{a}$ is

• A. 0.016
• B. $\frac{125}{2}$
• C. 0.16
• D. 0.064

Answer 1

The correct option is B

$\frac{125}{2}$

$\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$
$0.04\times 0.4\times a=(0.4\times 0.04\times \sqrt{b}{)}^2$ [squaring both sides]
$\frac{0.04\times 0.4\times a}{(0.4{)}^2\times (0.04{)}^2}=b$
$\frac{b}{a}=\frac{1}{\left(0.4\right)\times \left(0.04\right)}$
$\frac{b}{a}=\frac{10\times 100}{4\times 4}=\frac{1000}{16}=\frac{250}{4}=\frac{125}{2}$