The numerator and denominator of a fraction are in the ratio of 2 : 3. If 6 is subtracted from the numerator… · ABC26GN1761
Subject: General Aptitude · Chapter: Problems on Numbers
The numerator and denominator of a fraction are in the ratio of 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. The numerator of the original fraction is
(a)6
(b)18
(c)27
(d)36
Answer
Answer (as printed): B
Explanation
Let the fraction be $\frac{2 x}{3 x}$. Then, $\frac{2 x-6}{3 x}=\frac{2}{3} \times \frac{2 x}{3 x} \Leftrightarrow \frac{2 x-6}{3 x}$ $$=\frac{4 x}{9 x} \Leftrightarrow 18 x^{2}-54 x=12 x^{2}$$
Explanation as extracted from the printed page; notation may be imperfect.