Question:
Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
Solution:
Let the number be $x$.
According to tne question,
$\frac{x}{5}+30=\frac{x}{4}-30$
$\Rightarrow$ $\frac{x}{5}-\frac{x}{4}=-30-30 \quad\left[\right.$ transposing $\frac{x}{4}$ to LHS and 30 to RHS $]$
$\Rightarrow$ $\frac{4 x-5 x}{20}=-60$
$\Rightarrow$ $-x=-60 \times 20$ [by cross-multiplication]
$\therefore$ $x=1200$
Hence, the required number is 1200 .