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Concentration / Percentage Mixture

Introduction

பல real-world mixture problems-ல், ஒரு liquid அல்லது substance-ல் குறிப்பிட்ட concentration அல்லது percentage அளவில் ஒரு component (உதா: salt, alcohol, acid) இருக்கும். இந்த pattern, தேவையான concentration பெற எவ்வளவு pure substance அல்லது solution சேர்க்க வேண்டும் அல்லது அகற்ற வேண்டும் என்பதை கணக்கிட உதவுகிறது.

Dilution, strengthening மற்றும் concentration adjustment போன்ற கேள்விகளை விரைவாக தீர்க்க இந்த pattern-ஐ புரிந்துகொள்வது மிகவும் முக்கியம்.

Pattern: Concentration / Percentage Mixture

Pattern

Key concept: Pure substance அளவு = (Total quantity × Concentration%) / 100.

Concentration-ஐ mix அல்லது change செய்யும் போது:
1. Mix செய்வதற்கு முன் மற்றும் பின் உள்ள pure substance அளவை எப்போதும் track செய்யவும்.
2. Concentration (%) = (Pure substance அளவு ÷ Total mixture quantity) × 100.
3. Pure substance conservation பயன்படுத்தவும்: Pure before = Pure after.

Step-by-Step Example

Question

40-litre solution-ல் 25% alcohol உள்ளது. Solution-ஐ 40% alcohol ஆக மாற்ற எவ்வளவு pure alcohol சேர்க்க வேண்டும்?

Solution

  1. Step 1: கொடுக்கப்பட்ட தகவல்களை கண்டறியவும்

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

  2. Step 2: தற்போதைய pure alcohol அளவை கண்டறியவும்

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

  3. Step 3: x litres pure alcohol சேர்க்கப்படுகிறது எனக் கொள்ளவும்

    அப்போது total alcohol = (10 + x) L மற்றும் total solution = (40 + x) L.

  4. Step 4: Concentration formula பயன்படுத்தவும்

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

  5. Step 5: Equation-ஐ simplify செய்யவும்

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

  6. Final Answer:

    10 litres pure alcohol சேர்க்க வேண்டும்.

  7. Quick Check:

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

Quick Variations

1. Pure substance-க்கு பதிலாக water (அல்லது diluting agent) சேர்த்தால் concentration குறையும்.

2. Pure substance சேர்த்தால் concentration அதிகரிக்கும்.

3. Mixture-ன் ஒரு பகுதி replace செய்யப்பட்டால், replacement formula அல்லது successive dilution rule பயன்படுத்தவும்.

Trick to Always Use

  • Step 1 → “pure = total × percentage / 100” என்பதை எழுதிக்கொள்ளவும்.
  • Step 2 → Pure substance conservation பயன்படுத்தவும் (pure before = pure after).
  • Step 3 → Equation அமைத்து unknown quantity-ஐ கண்டறியவும்.

Summary

Summary

Concentration / Percentage Mixture pattern-ல்:

  • Concentration (%) = (Pure quantity ÷ Total quantity) × 100 என்பதை பயன்படுத்தவும்.
  • Mix செய்வதற்கு முன் மற்றும் பின் உள்ள pure substance அளவை சமமாக்கவும்.
  • Pure substance சேர்த்தால் concentration அதிகரிக்கும்; solvent சேர்த்தால் குறையும்.
  • Quick check: புதிய total மற்றும் pure values கொண்டு final concentration-ஐ மீண்டும் கணக்கிடவும்.

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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