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

Given, 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4.

⇒ 4a – 8 = b + 3

⇒ 4a – b = 11 ------ (1)

Also, when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3.

⇒ 3a + 18 = 2b

⇒ a + 6 = 2b -------- (2)

Multiplying eq2 by 4 and subtracting from eq1

⇒ 4a – b – 4a – 24 = 11 – 8b

⇒ 7b = 35

⇒ b = 5

Thus, a = 4

Fraction is 4/5