Let the numerator be ‘a’ and denominator be ‘b’

Given, sum of a numerator and denominator of a fraction is 18.

⇒ a + b = 18 ----- (1)

Also, if the denominator is increased by 2, the fraction reduces to 1/3.

⇒ a/(b + 2) = 1/3

⇒ 3a - b = 2 ------ (2)

Adding (1) and (2)

⇒ 4a = 20

⇒ a = 5

Thus, b = 13

Fraction is 5/13