The denominator of a fraction is 4 more than twice the numerator. When the numerator is increased by 3 and the denominator is decreased by 3, the fraction becomes $$\frac{2}{3}.$$ What is the difference between the denominator and numerator of the original fraction?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{x + 3}}{{2x + 4 - 3}} = \frac{2}{3} \cr & 3x + 9 = 4x + 2 \cr & x = 7 \cr & {\text{Original fraction}} \cr & \frac{x}{{2x + 4}} = \frac{7}{{18}} > 11 \cr} $$
Differentiate between numerator and denumerator = 11