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Basic Mixture Concept

Introduction

Mixture problems में दो या अधिक components को मिलाया जाता है जिनकी concentrations, costs या qualities अलग होती हैं। यह pattern ज़रूरी है क्योंकि यह बाकी mixture problems (जैसे alligation और replacement cases) की नींव बनाता है।

Weighted average से final mixture concentration निकालना समझना गणित और real-world दोनों में बहुत काम आता है।

Pattern: Basic Mixture Concept

Pattern

मुख्य विचार: Final concentration quantities के आधार पर individual concentrations का weighted average होता है।

उपयोग किया गया formula:
Final Concentration = (सभी pure component amounts का योग) ÷ (Total quantity)

Steps:
1. % को decimal में बदलें (अगर ज़रूरी हो)
2. हर quantity को उसकी concentration से multiply करें
3. सभी contributions जोड़कर total volume से divide करें

Step-by-Step Example

Question

आपके पास 30 litres की 20% acid solution और 10 litres की 50% acid solution है। Mixture में acid की final concentration निकालें।

Solution

  1. Step 1: दिए गए डेटा को पहचानें

    30 L @ 20% और 10 L @ 50%।

  2. Step 2: % को decimals में बदलें

    20% = 0.20, 50% = 0.50.

  3. Step 3: Pure acid content निकालें

    हर solution में pure acid:

    • पहले से: 30 × 0.20 = 6 L
    • दूसरे से: 10 × 0.50 = 5 L

  4. Step 4: Acid और total volume जोड़ें

    Total acid = 6 + 5 = 11 L; total volume = 30 + 10 = 40 L.

  5. Step 5: Final concentration निकालें

    Final concentration = (11 ÷ 40) × 100 = 27.5%.

  6. Final Answer:

    27.5%

  7. Quick Check:

    Final % (27.5%) - 20% और 50% के बीच है और 20% के थोड़ा पास है (क्योंकि उसकी quantity ज़्यादा थी)। ✅

Quick Variations

1. अगर एक liquid pure (100%) हो, तो वही formula लागू करें - उसका contribution उसका पूरा volume होगा।

2. Solids पर भी यही तरीका चलता है (जैसे salt + sand mixtures)।

3. जब एक quantity पानी (0%) हो, तो वह concentration को dilute करता है।

Trick to Always Use

  • Step 1 → % को decimal में convert करें (या % में ही consistently काम करें)।
  • Step 2 → Quantity × concentration हर component के लिए निकालें।
  • Step 3 → सारे results जोड़ें और total quantity से divide करें।
  • Step 4 → Percentage में बताने के लिए ×100 करें।

Summary

Summary

Basic Mixture Concept pattern में:

  • Final concentration = component concentrations का weighted average।
  • हर भाग की pure content = quantity × concentration से निकालें।
  • Total pure content ÷ total quantity = final strength।
  • Quick check: Final concentration हमेशा दोनों दी गई concentrations के बीच होती है।

Practice

(1/5)
1. A solution of 20 litres contains 25% sugar. How much pure sugar is in the solution?
easy
A. 5 litres
B. 4 litres
C. 6 litres
D. 3 litres

Solution

  1. Step 1: Identify Data

    Total solution = 20 L; concentration = 25%.

  2. Step 2: Convert to Decimal

    25% = 0.25.

  3. Step 3: Calculate Pure Sugar

    Pure sugar = 20 × 0.25 = 5 litres.

  4. Final Answer:

    Pure sugar = 5 litres → Option A.

  5. Quick Check:

    5 ÷ 20 = 0.25 → 25% ✅
Hint: Multiply total quantity by concentration fraction.
Common Mistakes: Dividing instead of multiplying or skipping % to decimal conversion.
2. A 40-litre mixture of milk and water contains 30% milk. If 10 litres of milk is added, find the new percentage of milk.
easy
A. 44%
B. 45%
C. 47.5%
D. 50%

Solution

  1. Step 1: Find Original Milk Quantity

    Milk = 40 × 0.30 = 12 L.

  2. Step 2: Add Extra Milk

    Added milk = 10 L → Total milk = 12 + 10 = 22 L.

  3. Step 3: Find New Total Volume

    Total mixture = 40 + 10 = 50 L.

  4. Step 4: Calculate New Concentration

    (22 ÷ 50) × 100 = 44%.

  5. Final Answer:

    New concentration = 44% → Option A.

  6. Quick Check:

    22 ÷ 50 = 0.44 → 44% ✅
Hint: Add pure quantity directly, then divide by new total.
Common Mistakes: Adding 10% instead of 10 litres of milk.
3. Two salt solutions of 10 litres each have concentrations 20% and 40%. What is the concentration after mixing them?
easy
A. 25%
B. 28%
C. 30%
D. 35%

Solution

  1. Step 1: Find Pure Salt in Each Solution

    First: 10 × 0.20 = 2 L; Second: 10 × 0.40 = 4 L.

  2. Step 2: Total Pure Salt

    2 + 4 = 6 L.

  3. Step 3: Total Volume

    10 + 10 = 20 L.

  4. Step 4: Find Final Concentration

    (6 ÷ 20) × 100 = 30%.

  5. Final Answer:

    Final concentration = 30% → Option C.

  6. Quick Check:

    Equal volumes → average of 20% and 40% = 30% ✅
Hint: For equal quantities, the final % is the average of both concentrations.
Common Mistakes: Using average formula when volumes differ.
4. A 15-litre solution has 6 litres of alcohol. What percentage of alcohol is in the solution?
medium
A. 30%
B. 35%
C. 45%
D. 40%

Solution

  1. Step 1: Identify Known Values

    Pure alcohol = 6 L; total solution = 15 L.

  2. Step 2: Apply Percentage Formula

    (6 ÷ 15) × 100 = 40%.

  3. Step 3: Interpret Result

    40% means 40 parts of every 100 are alcohol.

  4. Final Answer:

    Alcohol percentage = 40% → Option D.

  5. Quick Check:

    15 × 0.40 = 6 L → consistent ✅
Hint: Use (part ÷ total) × 100 to get percentage.
Common Mistakes: Dividing total by part instead of part by total.
5. A container has 25 litres of a 60% sugar solution. How much water must be added to make it a 40% solution?
medium
A. 10 litres
B. 12.5 litres
C. 15 litres
D. 20 litres

Solution

  1. Step 1: Find Initial Pure Sugar

    25 × 0.60 = 15 L of sugar.

  2. Step 2: Assume x Litres of Water Added

    New total volume = 25 + x.

  3. Step 3: Set Up Equation for New Concentration

    (15 ÷ (25 + x)) × 100 = 40.

  4. Step 4: Solve for x

    15 = 0.40 × (25 + x) → 15 = 10 + 0.4x → x = 12.5 L.

  5. Final Answer:

    Water to be added = 12.5 litres → Option B.

  6. Quick Check:

    Total = 37.5 L; 15 ÷ 37.5 = 0.4 → 40% ✅
Hint: Pure content stays constant; solve using (pure ÷ total) = target fraction.
Common Mistakes: Assuming total amount remains unchanged after adding water.

Mock Test

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