Correct Option: B

Method 1 to solve the question.
Let us assume the numerator be x.
Then the denominator will be 3x + 2.
According the question,
if the numerator as well as denominator is increased by one , the fraction becomes 1/3,
(x + 1)/(3x + 2 + 1) = 1/3
⇒ (x + 1)3 = 1(3x + 2 + 1)
⇒ 3x + 3 = 3x + 3
Since Left hand side equation is same to right hand side equation. So we cannot solve the equation and cannot determine the answer.

Method 2 to solve the question.
Let us assume the numerator be x and denominator be y.
According to question,
The denominator of a fraction is 2 more than thrice its numerator.
y = 3x + 2 .....................(1)
Again According to question,
if the numerator as well as denominator is increased by one , the fraction becomes 1/3.
(x + 1)/(y + 1) = 1/3
⇒ 3(x + 1) = y + 1
⇒ 3x + 3 = y + 1
⇒ y = 3x + 2............(2)
Since Equation (1) and (2) is same. So we cannot determine the number.

Method 3 to solve the question.
Hit and Trail method.
Solve all option one by one as per given question.
First took Option (A) 4/13
Numerator 4 in given fraction in Option (A)
The denominator of a fraction is 2 more than thrice its numerator.
So denominator = 2 + 4 x 3 = 2 + 12 = 14
So fraction will be 4/14 So this is wrong answer.
Now took Option (B) 3/11
Numerator 3 in given fraction in Option (B)
The denominator of a fraction is 2 more than thrice its numerator.
So denominator = 2 + 3 x 3 = 2 + 9 = 11
So fraction will be 3/11 So this is right answer.