Step 1: Analyze the reaction.
The reaction involves the addition of Br\(_2\) to a cycloalkene. The C : Br ratio is 3 : 1, indicating that three carbon atoms are involved for every one bromine atom in the product.
Step 2: Calculate the percentage of Br in the product.
For each mole of X, one mole of Br\(_2\) is consumed, and each molecule of the product contains 1 bromine atom for 3 carbon atoms. Therefore, the percentage of bromine in the product is:
\[
\text{Percentage of Br} = \frac{1}{3 + 1} \times 100 = 66\%.
\]
Final Answer:
\[
\boxed{66\%}.
\]