Question

The denominator of a fraction is $2$ less than twice the numerator. If the numerator denominator are both increased by $1$ the fraction become $\frac{3}{5}$. Find the fraction.

Answer 1

Let the numerator be $x$ then according to the questions, the denominator is $2$ less than twice the numerator,

So the fraction is

$\frac{x}{2x-2}$

Given, if both numerator and denominator are increased by $1$ then the fraction becomes $\frac{3}{5}$

i.e $\frac{x+1}{2x-2+1}=\frac{3}{5}$

$\frac{x+1}{2x-1}=\frac{3}{5}$

$5(x-1)=3(2x-1)$

$5x-5=6x-3$

$x=8$

.So, the fraction is $\frac{8}{(8\times 2)-2}=\frac{8}{15}$