Question

If the numerator of a fraction is multiplied by 2 and its denominator is increased by 1, it becomes 1. However, if the numerator is increased by 4 and denominator is multiplied by 2, the fraction becomes $\frac{1}{2}$. Find the fraction.

Answer 1

Let the fraction be $\frac{x}{y}$

Given, $\frac{2x}{y+1}=1$ $⟹2x=y+1$ -----(1)

$\frac{x+4}{2y}=\frac{1}{2}$ $⟹x+4=y$ -----(2)

Solving (1) and (2), we get,

$x=5$ and $y=9$

$\therefore \frac{5}{9}$ is the fraction.