Question

Solve the following:

If numerator is 2 less than denominator of a rational number and when 1 is substracted from numerator and denominator both, the rational number in its simplest form is $\frac{1}{2}$. What is the rational number?

Answer 1

Suppose denominator of a rational number be $x$.
Numerator=Denominator $-2=x-2$
According to the question,
$\frac{(x-2)-1}{x-1}=\frac{1}{2}$
$\Rightarrow 2(x-2-1)=x-1$
$\Rightarrow 2(x-3)=x-1$
$\Rightarrow 2x-6=x-1$
$\Rightarrow 2x-x=6-1$
$\therefore x=5$
Hence, denominator $=5$ and numerator $=5-2=3$
Thus, the rational number is $\frac{3}{5}.$