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Concentration / Percentage Mixture

Introduction

Many real-world mixture problems deal with liquids or substances that have a specific concentration or percentage of a component (like salt, alcohol, or acid). This pattern helps you calculate how much of a pure substance or solution to add or remove to achieve a desired concentration.

Understanding this pattern is essential for solving questions on dilution, strengthening, and concentration adjustment quickly.

Pattern: Concentration / Percentage Mixture

Pattern

The key concept: The amount of pure substance = (Total quantity × Concentration%) / 100.

When mixing or altering concentrations:
1. Always track the total amount of pure substance before and after mixing.
2. Concentration (%) = (Amount of pure substance ÷ Total mixture quantity) × 100.
3. Use conservation of pure substance: Pure before = Pure after.

Step-by-Step Example

Question

A 40-litre solution contains 25% alcohol. How much pure alcohol must be added to make the solution 40% alcohol?

Solution

  1. Step 1: Identify given data

    Total solution = 40 L, Alcohol concentration = 25%, New concentration = 40%.

  2. Step 2: Find current pure alcohol content

    Pure alcohol = 25% of 40 = (25/100) × 40 = 10 L.

  3. Step 3: Let x litres of pure alcohol be added

    Then total alcohol = (10 + x) L and total solution = (40 + x) L.

  4. Step 4: Apply concentration formula

    (10 + x)/(40 + x) × 100 = 40 → (10 + x) = 0.4(40 + x).

  5. Step 5: Simplify the equation

    10 + x = 16 + 0.4x → 0.6x = 6 → x = 10 L.

  6. Final Answer:

    10 litres of pure alcohol must be added.

  7. Quick Check:

    Total = 40 + 10 = 50 L → Alcohol = 10 + 10 = 20 L → (20/50)×100 = 40% ✅

Quick Variations

1. Adding water (or diluting agent) instead of pure substance decreases concentration.

2. Adding pure substance increases concentration.

3. If part of the mixture is replaced, use replacement formula or successive dilution rule.

Trick to Always Use

  • Step 1 → Write “pure = total × percentage / 100”.
  • Step 2 → Apply conservation of pure substance (pure before = pure after).
  • Step 3 → Set up equation and solve for unknown quantity.

Summary

Summary

In the Concentration / Percentage Mixture pattern:

  • Use concentration (%) = (Pure quantity ÷ Total quantity) × 100.
  • Always equate total pure substance before and after mixing or adding.
  • Adding pure substance increases concentration; adding solvent decreases it.
  • Quick check: Recalculate final concentration using new total and pure parts.

Practice

(1/5)
1. A 50-litre solution contains 20% sugar. How much pure sugar must be added to make the solution 40% sugar?
easy
A. 10.33 L
B. 16.67 L
C. 13.33 L
D. 15.67 L

Solution

  1. Step 1: Identify data

    Total = 50 L; current concentration = 20%; target = 40%.

  2. Step 2: Find current pure sugar

    Pure sugar = 20% of 50 = 10 L.

  3. Step 3: Let x L pure sugar be added

    New pure sugar = 10 + x; new total = 50 + x.

  4. Step 4: Set up equation

    (10 + x)/(50 + x) = 0.40 → 10 + x = 20 + 0.4x → 0.6x = 10 → x = 50/3 L = 16.67 L.

  5. Final Answer:

    Add 16.67 L (≈ 50/3 L) → Option B.

  6. Quick Check:

    Using exact value: (10 + 50/3) / (50 + 50/3) = (80/3) / (200/3) = 80/200 = 0.40 → 40% ✅
Hint: Set (pure before + added) ÷ (total before + added) = target fraction and solve for x.
Common Mistakes: Choosing the nearest option without checking exact fraction; forgetting to increase total volume.
2. A 60-litre acid solution contains 30% acid. How much pure water should be added to reduce acid concentration to 15%?
easy
A. 40 L
B. 60 L
C. 80 L
D. 90 L

Solution

  1. Step 1: Identify data

    Total = 60 L, Acid = 30%, Target = 15%.

  2. Step 2: Find pure acid

    (30/100)×60 = 18 L.

  3. Step 3: Let x L water be added

    Total = 60 + x; acid = 18 L.

  4. Step 4: Apply formula

    18/(60 + x) = 0.15 → 18 = 9 + 0.15x → 0.15x = 9 → x = 60 L.

  5. Final Answer:

    Add 60 L water → Option B.

  6. Quick Check:

    18/(60 + 60)=18/120=0.15=15% ✅
Hint: When diluting, pure amount is fixed - solve for total after dilution.
Common Mistakes: Reducing acid quantity when adding only water.
3. A 40-litre mixture contains 10% alcohol. How much pure alcohol should be added to make it 25% alcohol?
easy
A. 6 L
B. 8 L
C. 10 L
D. 12 L

Solution

  1. Step 1: Identify data

    Total = 40 L, Alcohol = 10%, Target = 25%.

  2. Step 2: Find current alcohol

    (10/100)×40 = 4 L.

  3. Step 3: Let x L pure alcohol be added

    Total = 40 + x; alcohol = 4 + x.

  4. Step 4: Apply formula

    (4 + x)/(40 + x) = 0.25 → 4 + x = 10 + 0.25x → 0.75x = 6 → x = 8 L.

  5. Final Answer:

    Add 8 L → Option B.

  6. Quick Check:

    (4 + 8)/(40 + 8)=12/48=25% ✅
Hint: Solve (pure before + x) ÷ (total + x) = target decimal.
Common Mistakes: Taking average instead of solving proportionally.
4. A 30-litre salt solution has 50% salt. How much of this must be replaced by pure water to make it 30% salt?
medium
A. 10 L
B. 12 L
C. 15 L
D. 18 L

Solution

  1. Step 1: Identify data

    Total = 30 L, Salt = 50%, Target = 30%.

  2. Step 2: Salt initially

    (50/100)×30 = 15 L.

  3. Step 3: Let x L be replaced with pure water

    Salt left = 15 - 0.5x; salt added = 0 (water has none).

  4. Step 4: Apply formula

    (15 - 0.5x)/30 = 0.30 → 15 - 0.5x = 9 → 0.5x = 6 → x = 12 L.

  5. Final Answer:

    Replace 12 L → Option B.

  6. Quick Check:

    (15 - 6)/30 = 9/30 = 30% ✅
Hint: Subtract removed pure part and divide remaining by total volume.
Common Mistakes: Forgetting to reduce pure substance after removal.
5. A 25-litre solution contains 40% acid. How much water should be added to reduce acid concentration to 25%?
medium
A. 10 L
B. 12 L
C. 15 L
D. 20 L

Solution

  1. Step 1: Identify data

    Total = 25 L, Acid = 40%, Target = 25%.

  2. Step 2: Find pure acid

    (40/100)×25 = 10 L.

  3. Step 3: Let x L water be added

    Total = 25 + x; acid = 10 L.

  4. Step 4: Apply formula

    10/(25 + x) = 0.25 → 10 = 6.25 + 0.25x → 0.25x = 3.75 → x = 15 L.

  5. Final Answer:

    Add 15 L water → Option C.

  6. Quick Check:

    10/(25 + 15)=10/40=25% ✅
Hint: Keep pure part same, increase total → use proportion to solve.
Common Mistakes: Using percent difference instead of fraction equation.

Mock Test

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