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

Given, if the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5

⇒ 10a = 6b – 30

⇒ 5a = 3b – 15 ---------- (1)

Also, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5

⇒ 5a + 40 = 4b -------- (2)

Subtracting eq2 from eq1

⇒ 5a – 5a – 40 = 3b – 15 – 4b

⇒ b = 25

Thus, 5a = 75 – 15

⇒ a = 12

Fraction is 12/25