Question

The ratio between the numerator and denominator in a fraction is 2:3. If 6 is subtracted from the numerator, the result is $\frac{2}{3}$ of the original fraction. The numerator of the original fraction is:

• A. 6
• B. 18
• C. 27
• D. 36
• E. None of these

Answer 1

The correct option is B

18

Let the fraction be $\frac{2x}{3x}$.

Then $\frac{2x-6}{3x}=\frac{2}{3}\times \frac{2x}{3x}\iff \frac{2x-6}{3x}=\frac{4x}{9x}\iff 18x^2-54x=12x^2$

Hence, the numerator of the original fraction = 2x =18