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 $$\frac{2}{3}$$. The fraction is :
Correct Answer: $$\frac{3}{8}$$
Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow x + y = 11.....(\text{i}) \cr & \Leftrightarrow \frac{{x + 1}}{{y - 2}} = \frac{2}{3} \cr & \Leftrightarrow 3\left( {x + 1} \right) = 2\left( {y - 2} \right) \cr & \Leftrightarrow 3x - 2y = - 7.....(\text{ii}) \cr} $$
Solving (i) and (ii), we get:
x = 3 and y = 8
So, the fraction is $$\frac{3}{8}$$
Then,
$$\eqalign{ & \Leftrightarrow x + y = 11.....(\text{i}) \cr & \Leftrightarrow \frac{{x + 1}}{{y - 2}} = \frac{2}{3} \cr & \Leftrightarrow 3\left( {x + 1} \right) = 2\left( {y - 2} \right) \cr & \Leftrightarrow 3x - 2y = - 7.....(\text{ii}) \cr} $$
Solving (i) and (ii), we get:
x = 3 and y = 8
So, the fraction is $$\frac{3}{8}$$