To solve this problem, follow these steps:

1. Find the total sum of the ages:

The average age of the three persons is 27 years. Since there are three persons, the total sum of their ages is:

$$\text{Total sum}=\text{Average}\times \text{Number of persons}=27\times 3=81$$

2. Use the given ratio to find the individual ages:

The ages are in the ratio 1:3:5. Let the ages be $x$, $3x$, and $5x$. The sum of these ages should equal the total sum we calculated:

$$x+3x+5x=81$$

Simplify to find $x$:

$$9x=81$$
$$x=\frac{81}{9}=9$$

3. Find the age of the youngest person:

The youngest person’s age is $x$, which is:

$$x=9$$

Thus, the age of the youngest person is 9 years, which corresponds to option B.