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Mixture/Alligation in % Form

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Introduction

சில aptitude கேள்விகளில் இரண்டு அல்லது அதற்கு மேற்பட்ட பொருட்களை கலப்பது (milk & water, alcohol & water, rice varieties போன்றவை) வெவ்வேறு percentages-ுடன் கொடுக்கப்படும்.

இவை mixture அல்லது alligation problems என அழைக்கப்படுகின்றன. இவை percentages-ஐ இணைத்து final concentration அல்லது mixing ratio-ஐ கண்டறியும் திறனை சோதிக்கின்றன.

Pattern: Mixture/Alligation in % Form

Pattern: Mixture/Alligation in % Form

Average % = (Quantity₁ × %₁ + Quantity₂ × %₂) ÷ (Quantity₁ + Quantity₂)

Alligation rule: (High% - Mean%) : (Mean% - Low%) = Ratio of mixing

Step-by-Step Example

Question

ஒரு mixture-ல் 30% milk உள்ளது, மீதி water. மற்றொரு mixture-ல் 70% milk உள்ளது. resulting mixture-ல் 50% milk இருக்க வேண்டுமெனில், இரண்டு mixture-களையும் எந்த ratio-வில் கலக்க வேண்டும்?

Solution

  1. Step 1: Percentages-ஐ அடையாளம் காணுங்கள்.

    முதல் mixture = 30% milk (low %)
    இரண்டாவது mixture = 70% milk (high %)
    Final mixture = 50% milk (mean %)

  2. Step 2: Alligation rule-ஐ பயன்படுத்துங்கள்.

    Sentence: (High - Mean) : (Mean - Low)
    Math: (70 - 50) : (50 - 30) = 20 : 20

  3. Step 3: Ratio-ஐ simplify செய்யுங்கள்.

    Ratio = 1 : 1

  4. Step 4: Final Answer.

    இரண்டு mixture-களும் 1 : 1 ratio-வில் கலக்க வேண்டும்.

  5. Step 5: Quick Check (average method).

    (30 + 70) ÷ 2 = 50% ✅

Quick Variations

Quantities கொடுக்கப்பட்டால்: weighted average formula-வை பயன்படுத்துங்கள். Example: 40% sugar solution 2 liters மற்றும் 60% solution 3 liters கலந்தால் → (2×40 + 3×60) ÷ (2+3) = 52%.

ஒரு solution pure ஆக இருந்தால்: pure milk-ஐ 100% என்றும், pure water-ஐ 0% என்றும் alligation-ல் எடுத்துக் கொள்ளுங்கள்.

Trick to Always Use

  • Step 1: Low %, High %, Mean % ஆகியவற்றை கண்டறியுங்கள்.
  • Step 2: (High - Mean) : (Mean - Low) formula-வை பயன்படுத்துங்கள்.
  • Step 3: இதுவே mixing ratio.
  • Step 4: Quantities கொடுக்கப்பட்டால் weighted average formula பயன்படுத்துங்கள்.

Summary

Mixture/Alligation pattern, weighted average formula அல்லது alligation rule மூலம் தீர்க்கப்படுகிறது.

Alligation formula: (High - Mean) : (Mean - Low)

  • High % = அதிக concentration.
  • Low % = குறைந்த concentration.
  • Mean % = தேவையான concentration.

பயிற்சியுடன், shortcut ratio method-ஐ பயன்படுத்தி mixture கேள்விகளை வேகமாக தீர்க்கலாம்.

Practice

(1/5)
1. A solution contains 20% sugar. If you take 1 liter of this solution, how much sugar is in it?
easy
A. 0.2 liters
B. 0.25 liters
C. 0.15 liters
D. 0.3 liters

Solution

  1. Step 1: Identify total and percentage

    Total solution = 1 liter, Sugar% = 20%.

  2. Step 2: Convert percent to fraction and multiply

    Sugar = (20 ÷ 100) × 1 = 0.2 liters.

  3. Final Answer:

    0.2 liters → Option A

  4. Quick Check:

    10% of 1 liter = 0.1 → 20% = 0.2 ✅
Hint: Sugar = (percentage ÷ 100) × total quantity.
Common Mistakes: Using 20 directly instead of converting to fraction of total.
2. A solution of 40% alcohol is mixed with 60% alcohol solution in equal quantities. What is the percentage of alcohol in the mixture?
easy
A. 48%
B. 50%
C. 52%
D. 54%

Solution

  1. Step 1: Note concentrations and ratio

    Two solutions: 40% and 60%, mixed in 1:1 ratio.

  2. Step 2: Take the simple average for equal quantities

    Average % = (40 + 60) ÷ 2 = 50%.

  3. Final Answer:

    50% → Option B

  4. Quick Check:

    Middle of 40% and 60% = 50% ✅
Hint: Equal quantities → just take simple average.
Common Mistakes: Forgetting that equal quantities means direct average.
3. In what ratio should a 20% acid solution and a 60% acid solution be mixed to get a 40% acid solution?
medium
A. 1:1
B. 2:1
C. 3:1
D. 1:2

Solution

  1. Step 1: Record low, high and mean percentages

    Low% = 20, High% = 60, Mean% = 40.

  2. Step 2: Apply alligation

    (High - Mean) : (Mean - Low) = (60 - 40) : (40 - 20) = 20 : 20.

  3. Final Answer:

    1:1 → Option A

  4. Quick Check:

    Equal mix of 20% and 60% → average = 40% ✅
Hint: Use alligation: (High-Mean):(Mean-Low).
Common Mistakes: Subtracting in wrong order or mixing up which side is high/low.
4. Two sugar solutions of 30% and 50% are mixed in the ratio 3:2. What is the percentage of sugar in the final mixture?
medium
A. 36%
B. 38%
C. 40%
D. 42%

Solution

  1. Step 1: Note quantities ratio and concentrations

    Quantities ratio = 3:2 → Total = 5 parts.

  2. Step 2: Compute weighted average

    Weighted average = (3×30 + 2×50) ÷ 5 = (90 + 100) ÷ 5 = 190 ÷ 5 = 38%.

  3. Final Answer:

    38% → Option B

  4. Quick Check:

    Value lies between 30% and 50% closer to 30% (since more of 30%) ✅
Hint: Weighted average = (Σ quantity × %) ÷ total quantity.
Common Mistakes: Taking simple average instead of weighted average.
5. A container has 25% alcohol solution. Another container has 45% alcohol solution. In what ratio should they be mixed to obtain 30% solution?
medium
A. 2:3
B. 3:2
C. 3:1
D. 4:1

Solution

  1. Step 1: Note low, high and desired percentages

    Low% = 25, High% = 45, Mean% = 30.

  2. Step 2: Apply alligation

    Alligation ratio = (45 - 30):(30 - 25) = 15:5 = 3:1.

  3. Final Answer:

    3:1 → Option C

  4. Quick Check:

    Mix 3 parts of 25% with 1 part of 45% → weighted average = (3×25 + 1×45)/4 = (75 + 45)/4 = 120/4 = 30% ✅
Hint: Alligation rule → (High-Mean):(Mean-Low).
Common Mistakes: Confusing ratio order (low vs high concentration).