Question

If 1 is added in the numerator and denominator, then fraction becomes $\frac{3}{4}$ and if we substract 1 from both numerator and denominator then becomes $\frac{2}{3}$, then find the fraction.

Answer 1

Let fraction be $\frac{x}{y},$ so

$\frac{x+1}{y+1}=\frac{3}{4}\Rightarrow 4x+1=3y+3$

$\Rightarrow 4x-3y=-1$ ...... (i)

And also

$\frac{x-1}{y-1}=\frac{2}{3}\Rightarrow 3x-3=2y-2$

$\Rightarrow 3x-2y=1$ ...... (ii)

On solving equations (i) and (ii), we get

$x=5$ and $y=7$

Thus, the fraction is $\frac{5}{7}$