Question

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

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Fifth}\mathrm{part}\mathrm{increased}\mathrm{by}5=\frac{\mathrm{x}}{5}+5 \\ \mathrm{Fourt}\mathrm{part}\mathrm{diminished}\mathrm{by}5=\frac{\mathrm{x}}{4}-5 \\ \therefore \frac{x}{5}+5=\frac{x}{4}-5 \\ \Rightarrow 5+5=\frac{x}{4}-\frac{x}{5} \\ \Rightarrow 10=\frac{5x-4x}{20} \\ \Rightarrow 10=\frac{x}{20} \\ \Rightarrow 200=x \\ \Rightarrow x=200 \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{is}200. \end{gathered}$$