- The sister is 12 years old.
- The person is three years older than the sister: \( 12 + 3 = 15 \).
- The brother is five years older than the person: \( 15 + 5 = 20 \).
- The mother is twice the age of the brother: \( 20 \times 2 = 40 \).
Thus, the mother’s age is 40 years.