To solve the problem, we can leverage key observations about the invariants in the system:

Key Observations

• Total water in both containers is always 10 liters (since no water is added or removed).
• Total alcohol in both containers is always 10 liters (same reason).
• Each container holds exactly 10 liters at all times (after each full operation: pour 1L from A→B then 1L from B→A, net volume remains 10L per container).

Invariant Relationship

Let:

• $W_A$ = water in container A
• $A_A$ = alcohol in container A
• $W_B$ = water in container B

Since container A has 10 liters:
$W_A + A_A = 10$ → $A_A = 10 - W_A$

Total water is 10 liters:
$W_A + W_B = 10$ → $W_B = 10 - W_A$

Ratio Calculation

From the above:
$A_A = W_B$ → $\frac{A_A}{W_B} = 1$

Answer: $\boxed{1}$

作者声明:本文包含人工智能生成内容。