Question

The numerator and denominator of a fraction is in the ratio 2:3.If 6 are subtracted from the numerator the value of the fraction becomes \(\frac 23\) of the original fraction.The numerator of the original fraction is,

• A. 16
• B. 21
• C. 18
• D. 30

Answer 1

The Correct Option is C

To solve this problem, let the numerator and denominator of the original fraction be \(2x\) and \(3x\) respectively, as given by the ratio \(2:3\). The fraction is then: \[ \frac{2x}{3x}=\frac{2}{3} \]

According to the problem, if 6 is subtracted from the numerator, the fraction becomes \(\frac{2}{3}\) of the original fraction: \[ \frac{2x-6}{3x}=\frac{2}{3}\cdot\frac{2x}{3x} \]

Calculate the right side: \[ \frac{2}{3}\cdot\frac{2}{3}=\frac{4}{9} \]

This gives us: \[ \frac{2x-6}{3x}=\frac{4}{9} \]

Cross-multiply to solve the equation: \[ 9(2x-6)=4(3x) \] \[ 18x-54=12x \] \[ 18x-12x=54 \] \[ 6x=54 \] \[ x=9 \]

The numerator is \(2x\), so substituting the value of \(x\): \[ 2x=2\cdot9=18 \]

Therefore, the numerator of the original fraction is 18.