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{:("Column A","A spirit and water soluti...

`{:("Column A","A spirit and water solution is sold in a market. The cost per liter of this solution is directly proportional to the part (fraction) or spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liters of water cost x dollars. A solution of 1 liter of spirit and 2 liters of water costs y dollars ","Column B"),(x,,y):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the cost of the spirit and water solutions based on the volume of spirit present in each solution. ### Step-by-Step Solution: 1. **Identify the Solutions**: - **Solution 1**: 1 liter of spirit + 1 liter of water - **Solution 2**: 1 liter of spirit + 2 liters of water 2. **Calculate Total Volume**: - For **Solution 1**: Total volume = 1 liter (spirit) + 1 liter (water) = 2 liters - For **Solution 2**: Total volume = 1 liter (spirit) + 2 liters (water) = 3 liters 3. **Calculate Fraction of Spirit**: - For **Solution 1**: Fraction of spirit = Volume of spirit / Total volume = 1 liter / 2 liters = 1/2 - For **Solution 2**: Fraction of spirit = Volume of spirit / Total volume = 1 liter / 3 liters = 1/3 4. **Establish Relationship Between Cost and Fraction of Spirit**: - The cost per liter of the solution is directly proportional to the fraction of spirit in the solution. This means: - Cost of Solution 1 (x) is proportional to 1/2 - Cost of Solution 2 (y) is proportional to 1/3 5. **Compare Costs**: - Since 1/2 (the fraction of spirit in Solution 1) is greater than 1/3 (the fraction of spirit in Solution 2), we can conclude that: - x > y 6. **Conclusion**: - Therefore, Column A (x) is larger than Column B (y). ### Final Answer: - The correct option is **(a)** if Column A is larger.
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