Question

If $x\%$ of 500 = $y\%$ of 300 and $x\%$ of $y\%$ of 200 = 60, then x = ?

• A. $10\sqrt{2}$
• B. $20\sqrt{2}$
• C. $15\sqrt{2}$
• D. $30\sqrt{2}$
• E. None of these

Answer 1

The correct option is D $30\sqrt{2}$

Here, $x\%$ of 500 = $y\%$ of 300
It can also written as:-
$\frac{x}{100}\times 500=\frac{y}{100}\times 30\Rightarrow 5x=3y$
$\Rightarrow 5x-3y=0$ $\dots \left(i\right)$
$\Rightarrow x=\frac{3}{5}\times y$
Again, $x\%$ of $y\%$ of 200 = 60
$\Rightarrow \frac{x}{100}\times \frac{y}{100}\times 200=60$
$x\times y=\frac{60\times 100}{2}$
$x\times y=3000$
Putting, $x=\frac{3}{5}\times y\Rightarrow \frac{3}{5}\times y\times y=3000$
$\Rightarrow y^2=1000\times 5\Rightarrow y=50\sqrt{2}$
and $x=\frac{3}{5}\times 50\sqrt{2}=30\sqrt{2}$