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Question
The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2. Find the rational number.
Solution
Let, the denominator of the rational number be x .
∴ The numerator of the rational number will be x - 3.
∴ The rational number = \[ \frac{x - 3}{x}\]
According to the question,
\[\frac{x - 3 + 2}{x + 5} = \frac{1}{2}\]
or \[\frac{x - 1}{x + 5} = \frac{1}{2}\]
or 2x - 2 = x + 5
or 2x - x = 5 + 2
or x = 7
\[ \therefore \text{ The rational number }= \frac{7 - 3}{7} = \frac{4}{7}\]
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