Question

The numerator of a fraction is $5$ less than the denominator. If the numerator is increased by $2$, the fraction reduces to $\frac{2}{3}$. Find the original fraction.

• A. $\frac{4}{9}$
• B. $\frac{11}{17}$
• C. $\frac{1}{13}$
• D. $\frac{17}{16}$

Answer 1

The correct option is A $\frac{4}{9}$

Let the fraction be $\frac{x-5}{x}$
Given, If the numerator is increased by $2$, then fraction $=\frac{x-3}{x}=\frac{2}{3}$
$\Rightarrow 3x-9=2x$
$\Rightarrow x=9$

Hence, the fraction is $\frac{9-5}{9}=\frac{4}{9}$