Question

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

Answer 1

Let numerator(N) of a fraction be $x.$

Then, denominator(D) $=2x-2$ [$\because$ $2\times$ N $=$ D $+$ 2 ]

$\therefore$ original Fraction $=\frac{x}{2x-2}$

Now according to the condition, if $3$ is added to the numerator and denominator, we have

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

$\Rightarrow 3x+9=4x-4+6$

$\Rightarrow 3x-4x=-4+6-9$

$\Rightarrow -x=-7$

$\therefore x=7$

Hence, the original fraction $=\frac{x}{2x-2}=\frac{7}{2\times 7-2}=\frac{7}{14-2}=\frac{7}{12}$