A fraction becomes $\dfrac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

Let numerator be x and denominator be y.

Given,

Denominator is 5 more than numerator.

∴ y = x + 5 ……(1)

Given,

A fraction becomes $\dfrac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator.

$\therefore \dfrac{x - 5}{y - 3} = \dfrac{1}{2} \\[1em] \Rightarrow 2(x - 5) = y - 3 \\[1em] \Rightarrow 2x - 10 = y - 3 \\[1em] \Rightarrow 2x - y = -3 + 10 \\[1em] \Rightarrow 2x - y = 7 \text{ …….(2)}$

Substituting value of y from equation (1) in (2), we get :

⇒ 2x - (x + 5) = 7

⇒ 2x - x - 5 = 7

⇒ x = 7 + 5

⇒ x = 12.

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

⇒ y = 12 + 5 = 17.

Fraction = $\dfrac{x}{y} = \dfrac{12}{17}$.

Hence, fraction = $\dfrac{12}{17}$.