Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations3 Marks
Question
Find the number whose fifth part increased by $5$ is equal to its fourth part diminished by $5.$
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Answer
Let the number be $x.$
Fifth part increased by $5=\frac{\text{x}}{5}+5$
Fourt part diminished by $5=\frac{\text{x}}{4}-5$
$\therefore\frac{\text{x}}{5}+5=\frac{\text{x}}{4}-5$
$\Rightarrow5+5=\frac{\text{x}}{4}-\frac{\text{x}}{5}$
$\Rightarrow10=\frac{5\text{x}-4\text{x}}{20}$
$\Rightarrow10=\frac{\text{x}}{20}$
$\Rightarrow10=\frac{\text{x}}{20}$
$\Rightarrow200=\text{x}$
$\Rightarrow\text{x}=200$
Therefore, the number is $200.$
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