# 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. - Mathematics

Numerical

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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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 9 Linear Equation in One Variable
Exercise 9.4 | Q 20 | Page 30