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Linear Equations in One Variable — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations in One Variable5 Marks
Question
A number whose fifth part increased by $5$ is equal to its fourth part diminished by $5$. Find the number.
✓

Answer

Let the requierd number $= x$
Then fifth part increased by $5=\frac{\text{x}}{5}+5$
fourth part diminished by $5=\frac{\text{x}}{4}+5$
According to the condition: $\frac{\text{x}}{5}+5=\frac{\text{x}}{4}-5$
$\Rightarrow\frac{\text{x}}{5}-\frac{\text{x}}{4}=-5-5$
$\Rightarrow\text{x}=\frac{4\text{x}-5\text{x}}{20}=-10$
$\Rightarrow-\frac{\text{x}}{20}=-10$
$\Rightarrow\text{x}=-10\times-20=200$
Required number $= 200$
Check: $\frac{200}{5}+5=\frac{200}{4}-5$
$\Rightarrow40 + 5 = 50 - 5$
$\Rightarrow 45 = 45$
Which is true. therefore our answer is correct.

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