Explanation:

- The total number of family members is 16, and the total average age is 30.

- This means the total age for all members is \(16 \times 30 = 480\).

- The ages of the two members excluded are the eldest and the youngest, with an age difference of 82 years.

- With the remaining 14 members, the average age is 28, so their total age is \(14 \times 28 = 392\).

- Therefore, the combined age of the eldest and youngest is \(480 - 392 = 88\).

- Let the youngest be \(x\), so the eldest is \(x + 82\).

- Equation: \(x + (x + 82) = 88\).

- Solving: \(2x + 82 = 88 \rightarrow 2x = 6 \rightarrow x = 3\).

- So the youngest is 3 years old and the eldest is \(3 + 82 = 85\) years old.

- The correct answer is Option 1: 85 years.