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?

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 %