Question

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.

Answer 1

Let the number = x

Then fifth part increased by $5=\frac{x}{5}+5$

Fourth part diminished by $5=\frac{x}{4}-5$

According to the condition :

$\frac{x}{5}+5=\frac{x}{4}-5$

$\Rightarrow \frac{x}{5}+5=\frac{x}{4}-5$

$\Rightarrow \frac{x}{5}-\frac{x}{4}=-5-5$

$\Rightarrow \frac{4x-5x}{20}=-10\Rightarrow -\frac{x}{20}=-10$

$\Rightarrow x=-10\times -20=200$

Check : $\frac{200}{5}+5=\frac{200}{4}-5$

$\Rightarrow 40+5=50-5$

$\Rightarrow 45=45$