# Two numbers are respectively 20% and 50% of a third number. What per cent is the first number of second?

• 110%
• 220%
• 330%
• 440%
$\begin{array}{rl}& \text{Let third number is x}.\\ & \text{Then}\phantom{\rule{thinmathspace}{0ex}}\text{first}\phantom{\rule{thinmathspace}{0ex}}\text{no}\text{.}\\ & 20\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}x=\frac{20x}{100}\\ & \text{Second}\phantom{\rule{thinmathspace}{0ex}}\text{number}\\ & =50\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}x=\frac{50x}{100}\\ & \text{Percent of first no of second no,}\\ & =\left[\frac{\left(\frac{20x}{100}\right)}{\left(\frac{50x}{100}\right)}\right]×100\\ & =\frac{\left(2×100\right)}{20}\\ & =40\mathrm{%}\end{array}$
$\begin{array}{rl}& \text{Let third number is x}.\\ & \text{Then}\phantom{\rule{thinmathspace}{0ex}}\text{first}\phantom{\rule{thinmathspace}{0ex}}\text{no}\text{.}\\ & 20\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}x=\frac{20x}{100}\\ & \text{Second}\phantom{\rule{thinmathspace}{0ex}}\text{number}\\ & =50\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}x=\frac{50x}{100}\\ & \text{Percent of first no of second no,}\\ & =\left[\frac{\left(\frac{20x}{100}\right)}{\left(\frac{50x}{100}\right)}\right]×100\\ & =\frac{\left(2×100\right)}{20}\\ & =40\mathrm{%}\end{array}$