A 15-litre mixture contains 20% alcohol, the remainder being water. If 3 litres of water are added, what is the percentage of alcohol in the new mixture?
Correct Answer: 16 2/3 %
Introduction / Context: We are adjusting a mixture by adding water only. Alcohol amount remains unchanged; the total volume increases, reducing alcohol percentage. This tests percentage and ratio understanding in mixtures.
Given Data / Assumptions:
- Initial volume = 15 L.
- Alcohol fraction = 20% ⇒ alcohol = 3 L, water = 12 L.
- Added water = 3 L.
Concept / Approach: New alcohol quantity stays 3 L; new total volume = 18 L. Percentage alcohol = (alcohol / total) * 100%.
Step-by-Step Solution: Initial alcohol = 0.20 * 15 = 3 L. Water increases from 12 L to 15 L. New total volume = 3 + 15 = 18 L. Alcohol percentage = (3 / 18) * 100% = 16 2/3 %.
Verification / Alternative check: Decimal form: 3/18 = 0.1666..., which is 16.67% approximately, consistent with 16 2/3 %.
Why Other Options Are Wrong: 17% and 18 1/2 % overestimate the alcohol content; 15% underestimates it. Only 16 2/3 % matches the exact calculation.
Common Pitfalls: Changing alcohol amount mistakenly or forgetting to update the total volume after adding water. Always hold the solute constant when diluting with pure solvent.
Final Answer: 16 2/3 %