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Mixture/Alligation in % Form

Introduction

कुछ aptitude questions में दो या ज़्यादा items को mix किया जाता है (जैसे milk-water, alcohol-water, rice varieties आदि) जिनमें percentages अलग-अलग होते हैं।

इन्हें mixture या alligation problems कहा जाता है। ये आपकी ability test करते हैं कि आप percentages को combine करके final concentration या mixing ratio निकाल सकते हैं या नहीं।

Pattern: Mixture/Alligation in % Form

Pattern

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

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

Step-by-Step Example

Question

एक mixture में 30% milk है और बाकी water। दूसरे mixture में 70% milk है। दोनों को किस ratio में मिलाया जाए ताकि final mixture में 50% milk हो?

Solution

  1. Step 1: Percentages पहचानें।

    पहला mixture = 30% milk (low %)
    दूसरा mixture = 70% milk (high %)
    Final mixture = 50% milk (mean %)

  2. Step 2: Alligation rule apply करें।

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

  3. Step 3: Ratio simplify करें।

    Ratio = 1 : 1

  4. Step 4: Final Answer.

    दोनों mixtures को 1 : 1 ratio में मिलाया जाएगा।

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

    (30 + 70) ÷ 2 = 50% ✅

Quick Variations

अगर quantities दी हों: Weighted average formula use करें। Example: 2 liters 40% sugar solution को 3 liters 60% से मिलाएं → (2×40 + 3×60) ÷ (2+3) = 52%.

अगर एक solution pure हो: Pure milk = 100% और pure water = 0% मानकर alligation करें।

Trick to Always Use

  • Step 1: Low %, high %, और mean % पहचानें।
  • Step 2: (High - Mean) : (Mean - Low) apply करें।
  • Step 3: यही mixing ratio होगा।
  • Step 4: Quantity-based problems में weighted average use करें।

Summary

Summary

Mixture/Alligation problems को या तो weighted average formula से या alligation rule से solve किया जाता है।

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

  • High % = strong concentration
  • Low % = weak concentration
  • Mean % = desired concentration

Regular practice से आप mixture वाले questions को shortcut ratio method से बहुत जल्दी solve कर पाएंगे।

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).

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