A sample of lotion has a total volume of 9 ml and contains 50% alcohol by volume. How much water (in ml) must be added to this 9 ml lotion so that the resulting mixture becomes a lotion containing 30% alcohol by volume?

Introduction / Context:
This question tests the core idea of mixture dilution: when you add a substance that contains 0% of the target ingredient (water has 0% alcohol), the quantity of the ingredient (alcohol) stays the same, but the total volume increases. The concentration changes only because the denominator (total volume) changes.

Given Data / Assumptions:

• Total lotion initially = 9 ml
• Alcohol concentration initially = 50%
• Final alcohol concentration needed = 30%
• Water added contains 0% alcohol

Concept / Approach:
Compute the initial amount of alcohol, keep it constant, and set it equal to 30% of the final total volume.

Step-by-Step Solution:

Verification / Alternative check:
After adding 6 ml water, total volume = 15 ml. Alcohol = 4.5 ml. Percentage = (4.5/15)*100 = 30%. Condition matches exactly.

Why Other Options Are Wrong:

Common Pitfalls:
Students often incorrectly reduce the alcohol amount when adding water, or apply percent directly to 9 ml instead of the final volume. Another common mistake is treating 30% as “reduce by 20 percentage points” without using the fraction equation.

Final Answer:
6 ml