In a fraction, twice the numerator is 2 more than the denominator.
Let the numerator be x
Denominator = 2x − 2
Therefore the fraction = x/2x − 2
Given when 3 is added to both the numerator and denominator, the fraction becomes 2/3.
Hence (x + 3)/(2x − 2 + 3) = 2/3
⇒ (x + 3)/(2x + 1) = 2/3
⇒ 3x + 9 = 4x + 2
⇒ x = 7
Therefore the fraction is 7/12.