To solve this problem, we need to set up an equation based on the information given and then solve for the fraction.

Let's assume the fraction is represented by x. According to the problem, the sum of the fraction and 4 times its reciprocal is equal to 13/3. We can write this as:

x + 4(1/x) = 13/3

To solve this equation, we can first simplify the right side of the equation by multiplying both the numerator and denominator of 13/3 by 3 to get:

x + 4(1/x) = (13/3)(3/3)
x + 4(1/x) = 39/9

Next, we can simplify the equation by multiplying both sides by 9 to get rid of the fraction:

9(x + 4(1/x)) = 9(39/9)
9x + 36/x = 39

Expanding the equation, we have:

9x^2 + 36 = 39x

Now, let's rearrange the equation to set it equal to zero:

9x^2 - 39x + 36 = 0

This is a quadratic equation, so we can solve it by factoring or by using the quadratic formula. Factoring this equation gives:

(3x - 4)(3x - 9) = 0

Setting each factor equal to zero, we have two possible solutions:

3x - 4 = 0 or 3x - 9 = 0

Solving these equations gives:

3x = 4 or 3x = 9

x = 4/3 or x = 9/3

However, we need to check if these solutions satisfy the original equation. Substituting x = 4/3 into the original equation:

(4/3) + 4(3/4) = 13/3
4/3 + 12/3 = 13/3
16/3 = 13/3

Since the equation is not true, x = 4/3 is not a valid solution.

Substituting x = 9/3 into the original equation:

(9/3) + 4(3/9) = 13/3
3 + 4/3 = 13/3
9/3 + 4/3 = 13/3
13/3 = 13/3

Since the equation is true, x = 9/3 = 3 is the valid solution.

Therefore, the fraction is 3/1, which is equivalent to 3. Therefore, the correct answer is option 'B' (3/4).