Question

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

• A. $\frac{3}{9}$
• B. $\frac{6}{9}$
• C. $\frac{3}{7}$
• D. None of these

Answer 1

The correct option is A $\frac{3}{9}$

let denominator $=x$

thus numerator $=x-6$

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

$3(x-3)=2x$

$3x-9=2x$

$x=9$

So denominator $=x=9$

thus numerator $\Rightarrow x-6=9-6=3$

Original fraction $=\frac{3}{9}$