The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3 . The fraction is :

Answer: Option C

Let the fraction be $$\frac{x}{y}$$
Then,
$$\begin{array}{rl}& \iff x+y=\mathrm{11.....}(\text{i})\\ & \iff \frac{x+1}{y-2}=\frac{2}{3}\\ & \iff 3\left(x+1\right)=2\left(y-2\right)\\ & \iff 3x-2y=-\mathrm{7.....}(\text{ii})\end{array}$$
Solving (i) and (ii), we get:
x = 3 and y = 8
So, the fraction is $$\frac{3}{8}$$