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.
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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