A fraction becomes $frac{9}{11}$, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes $frac{5}{6}$. What is the fraction?

Solve this question by options. Original fraction $=frac{7}{9}$ Adding 2 to numerator and denominator, fraction $=frac{9}{11}$ Adding 3 to numerator and denominator, fraction $=frac{10}{12}=frac{5}{6}$

Alternative:

Let the fraction be $frac{x}{y}$.

According to the question,

$frac{x+2}{y+2}=frac{9}{11}$

$frac{x+3}{y+3}=frac{5}{6}$

6x + 18 = 5y + 15

5y – 6x = 3 .....(2)

From equation (1) and (2)

x = 7, y = 9

$herefore$ Fraction number $=frac{x}{y}=frac{7}{9}$