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Find a number whose fifth part increased

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 .

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