Question

Question 98

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 $\frac{3}{5}.$