To determine the number of gallons of solution in Tank A and Tank B, we need to find the current amount of solution in each tank. This requires knowing their total capacities and the percentage they are currently full.

The problem states a key relationship between the capacities of the two tanks:

• Capacity of solution tank A is 70% of the capacity of tank B.
• Let $\text{Cap}_{\text{A}}$ represent the capacity of Tank A and $\text{Cap}_{\text{B}}$ represent the capacity of Tank B.
• Mathematically, this relationship is expressed as: $\text{Cap}_{\text{A}} = 0.70 \times \text{Cap}_{\text{B}}$.

Analyzing Statement I: Tank Fill Levels

Statement I provides information about the current fill levels of each tank:

• Tank A is 80% full.
• Tank B is 40% full.

From this statement, we can express the amount of solution in each tank:

• Solution in Tank A ($\text{Sol}_{\text{A}}$) = $0.80 \times \text{Cap}_{\text{A}}$
• Solution in Tank B ($\text{Sol}_{\text{B}}$) = $0.40 \times \text{Cap}_{\text{B}}$

If we substitute the relationship $\text{Cap}_{\text{A}} = 0.70 \times \text{Cap}_{\text{B}}$ (from the question) into the expression for $\text{Sol}_{\text{A}}$:

• $\text{Sol}_{\text{A}} = 0.80 \times (0.70 \times \text{Cap}_{\text{B}})$
• $\text{Sol}_{\text{A}} = 0.56 \times \text{Cap}_{\text{B}}$

With only Statement I, we can express the amount of solution in each tank in terms of $\text{Cap}_{\text{B}}$, but we do not have a specific numerical value for $\text{Cap}_{\text{B}}$. Therefore, Statement I alone is not sufficient to find the exact gallons of solution in Tank A and Tank B.

Analyzing Statement II: Tank A's Full Capacity

Statement II provides the maximum capacity of Tank A:

• Tank A if full contains 14,000 gallons of solution.
• This means $\text{Cap}_{\text{A}} = 14,000$ gallons.

Using the initial relationship given in the question ($\text{Cap}_{\text{A}} = 0.70 \times \text{Cap}_{\text{B}}$), we can now find the capacity of Tank B:

• $14,000 = 0.70 \times \text{Cap}_{\text{B}}$
• $\text{Cap}_{\text{B}} = \frac{14,000}{0.70}$
• $\text{Cap}_{\text{B}} = 20,000$ gallons.

So, we now know the capacities of both tanks:

• $\text{Cap}_{\text{A}} = 14,000$ gallons
• $\text{Cap}_{\text{B}} = 20,000$ gallons

However, Statement II does not provide any information about how *full* the tanks currently are. Without knowing the percentage they are filled, we cannot determine the current amount of solution in gallons. Therefore, Statement II alone is not sufficient.

Combining Statements I and II: Determining Gallons

Since neither statement alone is sufficient to answer the question, we combine the information provided by both statements.

From Statement II, we have the total capacities:

• $\text{Cap}_{\text{A}} = 14,000$ gallons
• $\text{Cap}_{\text{B}} = 20,000$ gallons

From Statement I, we know the current fill percentages:

• Tank A is 80% full.
• Tank B is 40% full.

Now, we can calculate the exact amount of solution currently in each tank:

• Gallons of solution in Tank A:
• $\text{Sol}_{\text{A}} = 80\% \text{ of } \text{Cap}_{\text{A}}$
• $\text{Sol}_{\text{A}} = 0.80 \times 14,000$ gallons
• $\text{Sol}_{\text{A}} = 11,200$ gallons

• Gallons of solution in Tank B:
• $\text{Sol}_{\text{B}} = 40\% \text{ of } \text{Cap}_{\text{B}}$
• $\text{Sol}_{\text{B}} = 0.40 \times 20,000$ gallons
• $\text{Sol}_{\text{B}} = 8,000$ gallons

By combining both statements, we are able to find the specific number of gallons of solution in Tank A and Tank B. Therefore, both statements I and II together are sufficient to answer the question.

Sufficiency Summary for Tank Problem

The final amounts are $\text{11,200}$ gallons in Tank A and $\text{8,000}$ gallons in Tank B.