The sum of numerator and denominator of a fraction is 22. If numerator is 8 less than its denominator; the fraction is :

1. $\dfrac{9}{13}$

2. $\dfrac{7}{15}$

3. $\dfrac{13}{9}$

4. $\dfrac{15}{7}$

Let numerator be x and denominator be y.

Given,

Sum of numerator and denominator of a fraction is 22.

∴ x + y = 22 ……..(1)

Given,

Numerator is 8 less than its denominator.

∴ y - x = 8 ……..(2)

Adding equation (1) and (2), we get :

⇒ (x + y) + y - x = 8 + 22

⇒ x - x + y + y = 30

⇒ 2y = 30

⇒ y = $\dfrac{30}{2}$ = 15.

Substituting value of y in equation (1), we get :

⇒ x + 15 = 22

⇒ x = 22 - 15 = 7.

Fraction = $\dfrac{x}{y} = \dfrac{7}{15}$.

Hence, Option 2 is the correct option.