Question

If $a^2$ $\%$ of $b=$ $b^3$ $\%$ of $c$ and $c^4$ $\%$ of $a=b$% of $b$, then the relation between $a$ and $b$ is

• A. $10000a^5=b^{12}$
• B. $a^9=b^{10}$
• C. $a^{12}=b^{21}$
• D. $10000a^{14}=b^{27}$

Answer 1

Answer: (B)

Given, $a^2$ $\%$ of $b=$ $b^3$ of $c$ $\Rightarrow \frac{a^2}{100}\times b=\frac{b^3}{100}\times c\Rightarrow a^{2}b=b^{3}c$ .....(i)
$c^4$ $\%$ of $a=b\%$ of $b$

$\Rightarrow \frac{c^4}{100}\times a=\frac{b}{100}\times b$

$\Rightarrow c^{4}a=b^2$
From (i), $c=\frac{a^2}{b^2}$
Putting the value of $c$ in(ii), we get

${\left(\frac{a^2}{b^2}\right)}^4\times a=b^2$

$\Rightarrow \frac{a^8\times a}{b^8}=b^2$

$\Rightarrow a^9=b^{10}$