Question

In a fraction twice the numerator is 2 more then the denominator. if 3 is added to a numerator and to the denominator the new fraction is $\frac{2}{3}$ find the original fraction.

Answer 1

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

Here the numerator and denominator is $x,y$ respectively

Given

Twice of $x$ is $2$ more than $y$

$⟹2x=y+2⟹y=2x-2$

And also if $3$ is added to both $x,y$ then the new fraction will be $2/3$

$⟹\frac{x+3}{y+3}=\frac{2}{3}$

$⟹\frac{x+3}{2x-2+3}=\frac{2}{3}$

$⟹3(x+3)=2(2x+1)$

$⟹3x+9=4x+2$

$⟹4x-3x=9-2$

$⟹x=7$

$y=2x-2=14-2=12$

The fraction is $\frac{7}{12}$