It is given that x is 20% lesser than m and y is 30% greater than n. Determine if $\dfrac{x}{y}$ is lesser or greater than $\dfrac{m}{n}$.
Show your working clearly. Answer ...

1. Express $x$ as a percentage of $m$.

Since $x$ is $20\%$ lesser than $m$,
$x=100\%m-20\%m=80\%m=0.8m=\frac{4}{5}m.$

2. Express $y$ as a percentage of $n$.

Since $y$ is $30\%$ greater than $n$,
$y=100\%n+30\%n=130\%n=1.3n=\frac{13}{10}n.$

3. Substitute into $\dfrac{x}{y}$ and compare with $\dfrac{m}{n}$.

$\frac{x}{y}=\frac{\frac{4}{5}m}{\frac{13}{10}n}$
$=\frac{4}{5}m\times \frac{10}{13n}$
$=\frac{8}{13}\times \frac{m}{n}.$
Since $\frac{8}{13}<1$,
$\frac{x}{y}<\frac{m}{n}.$