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Mixing Two Mixtures

Introduction

Sometimes you mix two already-prepared mixtures (each with its own concentration or price) to create a final mixture. This pattern teaches how to combine their pure parts correctly and find the resulting concentration or required quantities.

It's important for problems where two jars, solutions, or batches are combined - common in aptitude tests and real-life mixing tasks.

Pattern: Mixing Two Mixtures

Pattern

Key concept: Add the pure parts from each mixture to get the total pure part; then divide by total volume to find the resulting concentration.

Steps to apply:
1. Compute pure part in each mixture = (concentration% × quantity) / 100.
2. Add pure parts to get total pure content.
3. Add quantities to get 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. If both are combined, what is the concentration of sugar in the final mixture? Also, if you want final 40 L of mixture at that concentration, how much of A and B would you need in the same ratio?

Solution

  1. Step 1: Compute pure sugar in each mixture

    Mixture A pure = 30 × 20% = 30 × 0.20 = 6 L.

    Mixture B pure = 50 × 40% = 50 × 0.40 = 20 L.

  2. Step 2: Total pure sugar and 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: If final required = 40 L at same concentration (32.5%)

    We must use same ratio of A : B as original volumes = 30 : 50 = 3 : 5.

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

    Amount of A = 3 × 5 = 15 L; Amount of B = 5 × 5 = 25 L.

  5. Final Answer:

    Final concentration = 32.5%. For 40 L at same concentration use 15 L of A and 25 L of B.

  6. Quick Check:

    Pure in 15 L of A = 15×0.20 = 3 L. Pure in 25 L of B = 25×0.40 = 10 L. Total pure = 13 L. 13/40 = 0.325 → 32.5% ✅

Quick Variations

1. Given final volume and concentration - find how much of each to mix using ratio of pure parts.

2. Mixing by price: treat price per kg like concentration and compute weighted average cost.

3. One mixture added in parts repeatedly - use same pure-part addition logic each time.

Trick to Always Use

  • Step 1: Always convert percentages to pure quantities first (quantity × percentage /100).
  • Step 2: Work with pure amounts and volumes - combine them, then convert back to percent.
  • Step 3: When asked for a smaller final quantity at same concentration, keep the original A:B volume ratio.

Summary

Summary

In the Mixing Two Mixtures pattern:

  • Compute pure content in each mixture first: pure = quantity × (percentage/100).
  • Add pure contents and volumes separately, then divide to get final percentage.
  • To scale down to a required final volume at the same concentration, use the original volume ratio between the two mixtures.
  • Quick check by recomputing pure parts of scaled amounts and verifying the final percentage.

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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