Explanation:
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.