Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$. What is the original fraction equal to ?

Answer 1

Let denominator of the original fraction = x

Then numerator = x - 6

and fraction $=\frac{x-6}{x}$

According to the condition :

$\frac{x-6+3}{x}=\frac{2}{3}$

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

$\Rightarrow 3(x-3)=2x$ (By cross multiplication)

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

$\Rightarrow x=9$

$\therefore$ Original fraction $=\frac{x-6}{x}=\frac{9-6}{9}=\frac{3}{9}$

Check : $\frac{3+3}{9}=\frac{6}{9}=\frac{2}{3}$

Which is given. Therefore our answer is correct.