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

Given, fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2.

⇒ 3a – 3 = b – 1

⇒ b = 3a – 2 ------ (1)

Also, if 1 is added to both the numerator and denominator, it becomes 1/2.

⇒ b = 2a + 1 ---------- (2)

Equating (1) and (2)

⇒ 3a – 2 = 2a + 1

⇒ a = 3

Thus, b = 7

Fraction is 3/7