If $$\sqrt {0.04 \times 0.4 \times a} $$ = 0.004 × 0.4 × $$\sqrt b ,$$ then the value of $$\frac{a}{b}\,{\text{is?}}$$
A. $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 3}}$$
B. $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 4}}$$
C. $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 5}}$$
D. $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 6}}$$
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & {\text{ }}\sqrt {0.04 \times 0.4 \times a} = 0.004 \times 0.4 \times \sqrt b \cr & \Rightarrow \sqrt {\frac{4}{{100}} \times \frac{4}{{10}} \times a} = \frac{4}{{1000}} \times \frac{4}{{10}} \times \sqrt b \cr & \Rightarrow \frac{4}{{10}}\sqrt {\frac{a}{{10}}} = \frac{4}{{10}} \times \frac{4}{{1000}} \times \sqrt b \cr & \Rightarrow \frac{a}{{10}} = \frac{{16}}{{1000000}} \times b \cr & \Rightarrow \frac{a}{b} = \frac{{16 \times 10}}{{1000000}} \cr & \Rightarrow \frac{a}{b} = \frac{{16}}{{100000}} \cr & \Rightarrow \frac{a}{b} = 16 \times {10^{ - 5}} \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
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