Given information:
- The degree of hydrolysis of a salt of weak acid and weak base in its 0.1 M solution is 50%.
- The molarity of the solution is 0.2 M.

To determine the percentage hydrolysis of the salt, we need to understand the concept of hydrolysis and how it relates to the concentration of the solution.

Hydrolysis is a chemical reaction in which water molecules split a compound into its constituent ions. In the case of a salt of a weak acid and weak base, the cation comes from a weak base and the anion comes from a weak acid. When this salt is dissolved in water, hydrolysis occurs, resulting in the formation of the conjugate acid and base of the weak acid and weak base.

The degree of hydrolysis is defined as the extent to which the salt undergoes hydrolysis. It is usually expressed as the percentage of salt molecules that undergo hydrolysis in a given solution.

Using the given information, let's analyze the situation step by step:

1. Given that the degree of hydrolysis is 50%, this means that 50% of the salt molecules have undergone hydrolysis, while the remaining 50% remain unchanged.

2. The molarity of the solution is 0.2 M. This means that the concentration of the salt in the solution is 0.2 M.

3. Since the degree of hydrolysis is 50%, it implies that 50% of the salt molecules have reacted with water to form the conjugate acid and base. Therefore, the concentration of the conjugate acid and base would also be 0.1 M each (50% of 0.2 M).

4. The remaining 50% of the salt molecules remain unchanged, resulting in a concentration of the unreacted salt of 0.1 M (50% of 0.2 M).

5. Now, to determine the percentage hydrolysis of the salt, we compare the concentration of the hydrolyzed product (conjugate acid or base) to the initial concentration of the salt.

- The concentration of the hydrolyzed product (conjugate acid or base) is 0.1 M.
- The initial concentration of the salt is 0.2 M.

Therefore, the percentage hydrolysis can be calculated as (0.1 M / 0.2 M) × 100 = 50%.

Hence, the correct answer is option B - 50%.