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 $\frac{1}{2}.$ Find the rational number.

Answer 1

Let denominator of the given rational number = x

Then numerator = x - 3

$\therefore$ Rational number $=\frac{x-3}{x}$

Acording to the condition :

$\frac{x-3+2}{x+5}=\frac{1}{2}\Rightarrow \frac{x-1}{x+5}=\frac{1}{2}$

By cross multiplication

$2(x-1)=x+5\Rightarrow 2x-2=x+5$

$\Rightarrow 2x-x=5+2\Rightarrow x=7$

$\therefore$ Rational number $=\frac{x-3}{x}=\frac{7-3}{7}=\frac{4}{7}$