Difficulty: Medium
Correct Answer: 6 ml
Explanation:
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:
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:
Step 1: Alcohol initially = 50% of 9 ml = 0.50 * 9 = 4.5 ml Step 2: Let water added = x ml, so final volume = 9 + x ml Step 3: Alcohol amount stays 4.5 ml after adding water Step 4: Final concentration condition: 4.5 / (9 + x) = 30 / 100 = 0.30 Step 5: Solve: 4.5 = 0.30 * (9 + x) = 2.7 + 0.30x Step 6: 4.5 - 2.7 = 0.30x => 1.8 = 0.30x => x = 6Verification / 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:
4.5 ml: would make total 13.5 ml, alcohol% = 4.5/13.5 = 33.33%, not 30%. 3 ml: would make total 12 ml, alcohol% = 37.5%, too high. 9 ml: would make total 18 ml, alcohol% = 25%, too low. 15 ml: would make total 24 ml, alcohol% = 18.75%, far too low.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
Discussion & Comments