Question

A fraction becomes $\frac{2}{3}$, if $1$ is added to both its numerator and denominator. The same fraction becomes $\frac{1}{2}$, if $1$ is subtracted from both the numerator and denominator Such a fraction is:

Answer 1

Let the fraction be $\frac{x}{y}$
$\Rightarrow \frac{x+1}{y+1}=\frac{2}{3}$ ....(i)
and $\frac{x-1}{y-1}=\frac{1}{2}$ ...(ii)
Solving (i)and (ii) we have x=3, y=5
$\therefore$ Required fraction $=\frac{3}{5}$