Question

In a fraction twice the numerator is 2 more than the denominator . If 3 is added to the numerator and to the denomenator, the new fraction is $\frac{2}{3}.$ Find the origional fraction.

Answer 1

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

Twice the numerator$2x=2$ more than the denominator$=y+2$

$\Rightarrow y=2x-2$

$\Rightarrow$ Fraction$=\frac{x}{2x-2}$

Given:$\frac{x+3}{y+3}=\frac{2}{3}$

Substitute $y=2x-2$ in $\frac{x+3}{y+3}=\frac{2}{3}$ we get

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

$\Rightarrow \frac{x+3}{2x+1}=\frac{2}{3}$

$\Rightarrow 3x+9=4x+2$

$\Rightarrow 3x-4x=2-9$

$\therefore x=7$

Put $x=7$ in $y=2x-2$ we get $y=2\times 7-2=14-2=12$

$\therefore x=7,y=12$

$\therefore$ the original fraction is $\frac{7}{12}$