Directions: Read the information and answer the given questions. Eight…

In birth-year / age-ranking puzzles, first convert every birth year into an age relative to the reference year, then arrange the entire group into one strict oldest-to-youngest order. Every relational clue — a gap between two people, “X people between A and B”, “immediately before”, or a numeric property such as a perfect-cube age — becomes a constraint on that single order. Fix the most restrictive numeric clue first, test the remaining slots against every other clue, and discard any arrangement that breaks even one constraint until exactly one full order survives.

1. Compute each person's age with respect to 2025 from the given birth years (1966→59, 1976→49, 1982→43, 1989→36, 1997→28, 1998→27, 2006→19, 2012→13) and rank them from oldest (position 1) to youngest (position 8).

2. Among these ages, only 27 is a perfect cube (3³), so “Q's age is a perfect cube” fixes Q at position 6 (born 1998).

3. “Exactly one person is born between U and Q” means the position-gap between U and Q (position 6) is 2, so U is at position 4 or position 8.

4. “Exactly two people are born between U and W” means the position-gap between U and W is 3. Combined with “W is older than 20 years” (ruling out the two youngest positions, 7 and 8, and position 6 which is Q), testing U at position 4 forces W to position 1; testing U at position 8 forces W to position 5.

5. “Both P and V are younger than 45 years” rules out positions 1 and 2 (ages 59 and 49) for P and V, and “V was born in the year immediately before P” needs two adjacent positions from the ones still open. With U at position 4 and W at position 1, the only adjacent pair left at position ≥3 is positions 7 and 8, so V takes position 7 and P takes position 8.

6. The three remaining positions (2, 3, 5) go to R, S and T. “R's age is at most 20 years less than S's age” and “the age gap between T and S is at most 10 years, with S younger” together allow exactly one fit: T at position 2, S at position 3, R at position 5 — every other pairing of these three positions breaks one of the two gap clues.

7. Checking the alternative from step 4 (U at position 8, W at position 5) shows that no assignment of the remaining three positions to R, S and T can satisfy both age-gap clues at once, so that branch is eliminated and the position order from steps 5–6 is the unique solution.

8. Reading off the final order gives P's age (position 8) and T's age (position 2); their sum is the answer.

Every one of the nine clues — the two age-gap conditions, the perfect-cube age, both position-gap clues, the adjacency clue, and the two “younger than” conditions — holds against this order, confirming it is the unique valid arrangement.

P's age is 13 and T's age is 49, so the sum of their ages is 13 + 49 = 62 years.