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Mixing Two Mixtures

Introduction

कई बार दो तैयार mixtures (हर एक का अपना concentration या price होता है) को मिलाया जाता है ताकि एक final mixture बने। यह pattern सिखाता है कि pure parts को सही तरीके से कैसे जोड़ें और resulting concentration या required quantities कैसे निकालें।

यह उन सवालों के लिए महत्वपूर्ण है जहाँ दो jars, solutions या batches को combine किया जाता है - aptitude tests और real-life दोनों में बहुत common है।

Pattern: Mixing Two Mixtures

Pattern

मुख्य विचार: दोनों mixtures के pure parts को जोड़ें; फिर total volume से divide करके final concentration निकालें।

Steps:
1. हर mixture में pure part = (concentration% × quantity) / 100.
2. Pure parts जोड़ें → total pure content।
3. Quantities जोड़ें → total volume।
4. Resulting concentration (%) = (Total pure ÷ Total volume) × 100.

Step-by-Step Example

Question

Mixture A: 30 L at 20% sugar. Mixture B: 50 L at 40% sugar. दोनों को मिलाने पर final mixture की sugar concentration क्या होगी? साथ ही, अगर आपको इसी concentration वाला 40 L mixture चाहिए हो, तो उसी ratio में A और B कितनी मात्रा लेनी होगी?

Solution

  1. Step 1: दोनों mixtures में pure sugar निकालें

    Mixture A: 30 × 20% = 30 × 0.20 = 6 L

    Mixture B: 50 × 40% = 50 × 0.40 = 20 L

  2. Step 2: Total pure sugar और total volume

    Total pure = 6 + 20 = 26 L

    Total volume = 30 + 50 = 80 L

  3. Step 3: Resulting concentration

    Concentration = (26 ÷ 80) × 100 = 0.325 × 100 = 32.5%

  4. Step 4: अगर final 40 L चाहिए उसी concentration (32.5%) पर

    Original ratio of A:B = 30 : 50 = 3 : 5

    Total parts = 3 + 5 = 8 → एक part = 40 ÷ 8 = 5 L

    A = 3 × 5 = 15 L; B = 5 × 5 = 25 L

  5. Final Answer:

    Final concentration = 32.5%. 40 L mixture के लिए 15 L of A और 25 L of B लें।

  6. Quick Check:

    A (15 L) pure = 15×0.20 = 3 L; B (25 L) pure = 25×0.40 = 10 L → total pure = 13 L → 13/40 = 32.5% ✅

Quick Variations

1. Final volume और concentration दिए हों तो pure parts के ratio से दोनों mixtures की मात्रा निकालें।

2. Price-mixing में price per kg को concentration की तरह treat करें और weighted average cost निकालें।

3. एक mixture को बार-बार parts में जोड़ने पर भी pure-part addition logic ही लागू होता है।

Trick to Always Use

  • Step 1: सबसे पहले percentages को pure quantities में बदलें (quantity × percentage / 100)।
  • Step 2: Pure amounts और volumes के साथ काम करें - उन्हें जोड़कर प्रतिशत में बदलें।
  • Step 3: Smaller final quantity चाहिए हो तो original A:B volume ratio बनाए रखें।

Summary

Summary

Mixing Two Mixtures pattern में:

  • हर mixture का pure content निकालें: pure = quantity × (percentage/100).
  • Pure contents और volumes को अलग-अलग जोड़ें, फिर divide करके final percentage निकालें।
  • Same concentration वाले smaller batch के लिए original volume ratio का उपयोग करें।
  • Scaled amounts में pure parts दोबारा check करके final percentage verify करें।

Practice

(1/5)
1. Mixture A: 10 L at 20% sugar. Mixture B: 30 L at 50% sugar. If both are combined, what is the concentration of sugar in the final mixture?
easy
A. 42.5%
B. 40%
C. 45%
D. 50%

Solution

  1. Step 1: Compute pure sugar in each mixture

    Mixture A pure = 10 × 0.20 = 2 L. Mixture B pure = 30 × 0.50 = 15 L.

  2. Step 2: Add pure parts and volumes

    Total pure = 2 + 15 = 17 L. Total volume = 10 + 30 = 40 L.

  3. Step 3: Find final concentration

    Concentration = (17 ÷ 40) × 100 = 42.5%.

  4. Final Answer:

    42.5% → Option A.

  5. Quick Check:

    17/40 = 0.425 → 42.5% ✅
Hint: Convert each mixture to its pure part, add them, then divide by total volume.
Common Mistakes: Averaging percentages without weighting by volumes.
2. Mixture A: 20 L at 10% concentration. Mixture B: 20 L at 30% concentration. If both are combined, what volume of A and B is needed to make 20 L of the final mixture at the same concentration?
easy
A. 10 L of A and 10 L of B
B. 8 L of A and 12 L of B
C. 5 L of A and 15 L of B
D. 12 L of A and 8 L of B

Solution

  1. Step 1: Compute original combined concentration

    Pure in A = 20×0.10 = 2 L; Pure in B = 20×0.30 = 6 L. Total pure = 8 L; total volume = 40 L → concentration = 8/40 = 20%.

  2. Step 2: To get 20 L at same concentration, keep original A:B volume ratio

    Original volumes A:B = 20:20 = 1 : 1.

  3. Step 3: Scale ratio to 20 L

    Total parts = 1 + 1 = 2 → one part = 20 ÷ 2 = 10 L → A = 10 L, B = 10 L.

  4. Final Answer:

    10 L of A and 10 L of B → Option A.

  5. Quick Check:

    Pure = 10×0.10 + 10×0.30 = 1 + 3 = 4 L → 4/20 = 0.20 → 20% ✅
Hint: When scaling to a smaller final volume at same concentration, use the original volume ratio.
Common Mistakes: Mixing different ratios instead of preserving the original ratio.
3. Mixture A: 5 L at 60% purity. Mixture B: 15 L at 20% purity. If combined, what is the purity of the final mixture?
easy
A. 25%
B. 30%
C. 35%
D. 40%

Solution

  1. Step 1: Find pure part in each mixture

    Pure in A = 5×0.60 = 3 L. Pure in B = 15×0.20 = 3 L.

  2. Step 2: Add pure parts and volumes

    Total pure = 3 + 3 = 6 L. Total volume = 5 + 15 = 20 L.

  3. Step 3: Compute final purity

    Purity = (6 ÷ 20) × 100 = 30%.

  4. Final Answer:

    30% → Option B.

  5. Quick Check:

    6/20 = 0.30 → 30% ✅
Hint: Equal pure parts can still yield low overall purity if total volume is large.
Common Mistakes: Forgetting to weight by volume when adding percentages.
4. You have 25 L of a 12% solution (Mixture A). How many litres of a 48% solution (Mixture B) must be added so that the resulting solution is 20%?
medium
A. 5.14 L
B. 6.14 L
C. 7.14 L
D. 8.14 L

Solution

  1. Step 1: Compute pure part in A

    Pure in A = 25 × 0.12 = 3 L.

  2. Step 2: Let x = litres of 48% B added

    Pure added = 0.48x; new total volume = 25 + x.

  3. Step 3: Form equation for 20%

    (3 + 0.48x)/(25 + x) = 0.20 → 3 + 0.48x = 5 + 0.20x → 0.28x = 2 → x = 2 / 0.28 = 7.142857... L.

  4. Final Answer:

    Approximately 7.14 L of Mixture B → Option C.

  5. Quick Check:

    Pure after ≈ 3 + 0.48×7.14 = 3 + 3.428 ≈ 6.428; total ≈ 32.14 → 6.428/32.14 ≈ 0.20 → 20% ✅
Hint: Set up (pure A + pure B) ÷ (vol A + vol B) = desired fraction and solve for the unknown volume.
Common Mistakes: Failing to convert percentages to decimals before calculating pure parts.
5. Mixture A: 18 L at 12% metal. Mixture B: 12 L at 48% metal. If both are combined, what is the metal percentage in the final mixture?
medium
A. 24.4%
B. 26.8%
C. 27.8%
D. 26.4%

Solution

  1. Step 1: Compute pure metal in each mixture

    Pure in A = 18 × 0.12 = 2.16 L. Pure in B = 12 × 0.48 = 5.76 L.

  2. Step 2: Add pure parts and volumes

    Total pure = 2.16 + 5.76 = 7.92 L. Total volume = 18 + 12 = 30 L.

  3. Step 3: Compute final percentage

    Percentage = (7.92 ÷ 30) × 100 = 26.4%.

  4. Final Answer:

    26.4% → Option D.

  5. Quick Check:

    7.92/30 = 0.264 → 26.4% ✅
Hint: Always convert percentages to actual pure quantities before adding.
Common Mistakes: Rounding intermediate values too early and losing precision.

Mock Test

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