The sum of the numerator and the 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:

$\frac{3}{8}$

Let us consider that fraction is = \(\frac{A}{B}\)

A + B = 11      ----(1)

ATQ,

\(\frac{A + 1 }{B - 2 }\) = \(\frac{2}{3}\)

3A + 3 = 2B - 4

3A - 2B = -7       -----(2)

Multiply equation 1 by 2 and add equation 1 and 2 ,

2A + 3A = -7 + 22

5A = 15

A = 3

Put A in equation 1 ,

3 + B = 11

B = 8

So, The fraction = \(\frac{3}{8}\)

The correct answer is Option (3) → $\frac{3}{8}$