Question : If $\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$, then $\frac{a}{b}$ is equal to:
Option 1: 0.0025
Option 2: 0.025
Option 3: 0.25
Option 4: 0.00025
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Correct Answer: 0.025
Solution :
$\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$
On squaring both sides,
⇒ $ 0.05\times 0.5 \times a = 0.5 \times 0.05 \times 0.5 \times 0.05 \times b$
⇒ $a = 0.5 \times 0.05 \times b$
⇒ $\frac{a}{b} = 0.5 \times 0.05 = 0.025$
Hence, the correct answer is 0.025.
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