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Question
A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.
Solution
Let the number be x .
According to the question,
\[\frac{x}{5} + 5 = \frac{x}{4} - 5\]
\[\text{ or }\frac{x}{5} - \frac{x}{4} = - 5 - 5\]
\[\text{ or }\frac{4x - 5x}{20} = - 10\]
or - x = - 200 [After cross multiplication]
or x = 200
Thus, the number is 200.
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