The numerator and denominator of a fraction are in the ratio 3 : 4. If 9 is subtracted from the numerator, the resulting fraction in $$\frac{2}{3}$$ of the original fraction. The numerator of the original fraction is

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{fraction}}\,{\text{be}}\,\frac{{3k}}{{4k}} \cr & \therefore \frac{{ {3k - 9} }}{{4k}} = {\frac{2}{3}} \cr & \therefore 9k - 27 = 8k \cr & \therefore k = 27 \cr } $$