Arrange by age and by wealth (decreasing): P, Q, R, and S are four males. • P is the eldest but not the poorest. • R is the richest but not the eldest. • Q is older than S, but not older than P or R. • P is richer than Q, but not richer than S. Find the decreasing order (oldest→youngest) and (richest→poorest).

Introduction / Context:
This classic two-criterion ranking puzzle asks you to produce two separate orders—by age and by wealth—given comparative constraints. The key is to keep the two orderings independent and avoid mixing statements across criteria.

Given Data / Assumptions:

• Age statements: P is eldest; R is not eldest; Q older than S, but Q is not older than P or R ⇒ R is older than Q; all ages distinct.
• Money statements: R is richest; P richer than Q but not richer than S ⇒ S > P > Q; since R is richest, overall: R > S > P > Q; all amounts distinct.

Concept / Approach:
Treat age and money as two separate partial orders. For age, “P eldest” and “Q not older than P or R” forces R above Q, giving P > R > Q > S. For money, combine “R richest” with “S > P > Q” to get R > S > P > Q.

Step-by-Step Solution:

Verification / Alternative check:
Try to violate any relation: making Q older than R contradicts “Q is not older than R.” Making P richer than S contradicts “P is not richer than S.” The found orders satisfy all constraints simultaneously.

Why Other Options Are Wrong:

• Orders placing Q above R in age or P above S in wealth break the given conditions.
• Any option with different sequences fails at least one bullet.

Common Pitfalls:
Mixing age and wealth statements (e.g., using “richest” to infer age). Keep dimensions separate, then pick the option that matches both.

Final Answer:
PRQS (age), RSPQ (money)