Question

The numerator and denominator of a fraction are in the ratio $2:3$. If $6$ is subtracted from the numerator the result is a fraction that has a value $\frac{2}{3}$ of the original fraction. What is the numerator of the original fraction?

• A. $14$
• B. $16$
• C. $18$
• D. $20$

Answer 1

The correct option is C $18$

Let the numerator and denominator of the fraction be $2x$ and $3x$
Therefore, the original fraction is $\frac{2x}{3x}$
Given, $\frac{2x-6}{3x}=\frac{2}{3}\times \frac{2x}{3x}$

$\Rightarrow \frac{2x-6}{3x}=\frac{4}{9}$

$\Rightarrow 18x-54=12x$

$\Rightarrow 6x=54$

$\Rightarrow x=9$
The numerator of the fraction is $2\times 9=18$