Question

Question 2 (i)
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?

Answer 1

Let the fraction be $\frac{x}{y}$
According to the question, $\frac{x+1}{y-1}=1$
$\Rightarrow$ x - y = -2 ... (i)
$\frac{x}{y+1}=\frac{1}{2}$
$\Rightarrow$ 2x - y = 1 ... (ii)
Subtracting equation (i) from equation (ii), we get
x = 3 ... (iii)
Putting this value in equation (i), we get
3 - y = -2
$\Rightarrow$ -y = -5
$\Rightarrow$ y = 5
Hence, the fraction is $\frac{3}{5}$.