Ages (two linked snapshot ratios): The present ratio of A : B is 5 : 3. Also, A's age 4 years ago equals B's age 4 years hence. Find the ratio of A's age 4 years hence to B's age 4 years ago.

Introduction / Context:
The problem binds two people's ages across different time points. Once the present ratio is parameterized, the cross-time equality determines the scale, and the requested ratio follows with simple arithmetic.

Given Data / Assumptions:

• Present: A : B = 5 : 3 ⇒ A = 5k, B = 3k.
• Constraint: A − 4 = B + 4 ⇒ A = B + 8.

Concept / Approach:
Combine A = 5k and B = 3k with A = B + 8 to find k, then compute A + 4 and B − 4 and take the ratio requested.

Step-by-Step Solution:

Verification / Alternative check:
Check the cross-time equality: A − 4 = 16 and B + 4 = 16 (✓).

Why Other Options Are Wrong:
They contradict either the present 5 : 3 ratio or the A − 4 = B + 4 condition.

Common Pitfalls:
Applying the +4 and −4 to the wrong person, which inverts the intended equality.

Final Answer:
3 : 1