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, then this becomes $\frac{2}{3}$. The fraction is -

Explanation

Let the fraction = $\frac{x}{y}$ As per the question $x + y = 11$ ......... (i) And, $\frac{x+1}{y-2} = \frac{2}{3}$ $3x + 3 = 2y - 4$ $3x - 2y = -7$ ...........(ii) From equation (i) and (ii) – $x = 3$ and $y = 8$ Hence, fraction = $\frac{x}{y} = \frac{3}{8}$. Age