Question

Find a number whose fifth part increased by $30$ is equal to its fourth part decreased by $30$.

Answer 1

Let the number be $x$
Its fifth part is $=\frac{x}{5}$
Its fourth part is $=\frac{x}{4}$
According to the given condition,
$\left(\frac{X}{5}\right)+30=\left(\frac{X}{4}\right)-30$
$\left(\frac{X}{5}\right)-\left(\frac{X}{4}\right)=-30-30$

$\frac{4X-5X}{20}=-60$
$-X=-60\times 20$
$-X=-1200$
$X=1200.$

Hence, the number is $1200.$