Diluting a 15-L mixture by adding water: A 15-liter mixture contains 20% alcohol (and 80% water). If 3 liters of water are added, what is the new percentage of alcohol?
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A17%
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B16 2/3%
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C18 1/2%
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D15%
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E14 2/3%
Answer
Correct Answer: 16 2/3%
Explanation
Introduction / Context: Adding water does not change the absolute alcohol quantity, only the total volume. Therefore, the new percentage is alcohol mass divided by the increased total volume, expressed as a percentage.
Given Data / Assumptions:
- Initial alcohol = 20% of 15 L = 3 L.
- Added water = 3 L.
- New total volume = 18 L.
Concept / Approach: New alcohol % = (unchanged alcohol) / (new total) * 100%. Substitute the values and reduce the fraction to a mixed number if needed.
Step-by-Step Solution:
Alcohol remains 3 L.New total = 15 + 3 = 18 L.Alcohol % = 3/18 * 100% = 1/6 * 100% = 16 2/3%.Verification / Alternative check: Decimal form: 0.1666… × 100% = 16.666…%, which matches 16 2/3%.
Why Other Options Are Wrong: They assume changed alcohol amount or use incorrect total volume after addition.
Common Pitfalls: Reducing alcohol amount by 20% of 3 L incorrectly; the alcohol content is unchanged by adding pure water.
Final Answer: 16 2/3%