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

Given, sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3.

⇒ a + b = 2a + 4

⇒ b – a = 4 -------- (1)

Also,

⇒ 3a + 9 = 2b + 6

⇒ 3a – 2b = - 3 ------(2)

Multiplying eq1 by 2 and adding to eq1

⇒ 2b – 2a + 3a – 2b = 8 - 3

⇒ a = 5

Thus b = 9

Fraction is 5/9