🧪 Mixture and Alligation PDF with Shortcut Tricks, Questions, PYQs, MCQs with Detailed Solutions – Free Download Updated Latest 2025

Mixture and Alligation PDF : Are you aiming to score high in Quantitative Aptitude for competitive exams like SSC, IBPS, SBI, CAT, CDS, UPSC, Railways, and more? Then mastering Mixture and Alligation is non-negotiable. It’s one of the most scoring and shortcut-friendly topics in arithmetic.

To help you out, GovernmentAdda.com offers a FREE Mixture and Alligation PDF that includes:

✅ Shortcut Techniques
✅ PYQs (Previous Year Questions)
✅ 100+ High-Level MCQs
✅ Diagrams + Conceptual Clarity
✅ Detailed Solutions for Every Question

📥 Download Free Mixture and Alligation PDF by GovernmentAdda.com

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📘 Table of Contents

1. What is Mixture and Alligation?
2. Importance in Competitive Exams
3. Shortcut Tricks for Mixture and Alligation
4. Must-Know Formulas
5. PYQs with Answers
6. 10+ MCQs with Detailed Solutions
7. Free PDF Download Link
8. FAQs

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📚 What is Mixture and Alligation?

Mixture and Alligation is a concept used to determine the ratio in which two or more ingredients (of different costs or concentrations) are mixed to obtain a desired cost or concentration.

It’s widely used in:

• Cost price and selling price comparisons
• Milk and water mixtures
• Alcohol dilution problems
• Profit-loss calculations

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🎯 Importance of Mixture and Alligation in Exams

Exam	Expected Questions	Difficulty Level
SSC CGL/CHSL	1–3	Moderate
IBPS/SBI PO	1–2	Moderate
CAT/XAT	2–3	High
CDS/NDA	2–4	Moderate
Railways	1–3	Moderate

It’s a frequently tested topic that can be cracked with one diagrammatic formula using the Alligation Rule.

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⚡ Shortcut Tricks for Mixture and Alligation

🔹 Alligation Rule (For Two Quantities)

To mix two items (say milk and water, or two solutions) at different costs or concentrations:

📌 Formula:

C1         C2
   \     /
    \   /
     \ /
      X
     / \
    /   \
   /     \
CP      CQ

Where:

• C1 = cost/concentration of 1st quantity
• C2 = cost/concentration of 2nd quantity
• X = Mean cost/concentration
• CP = C2 – X
• CQ = X – C1

📌 Ratio of quantities to be mixed = CP : CQ

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🔹 Trick Example:

Mix milk at ₹40/litre and ₹60/litre to get ₹50/litre.

40       60
   \     /
    \   /
     \ /
     50
     / \
   10   10

So, the ratio = 1:1

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📌 Must-Know Formulas

Concept	Formula
Mean price (two mixtures)	(C1Q1 + C2Q2) / (Q1 + Q2)
Alligation Rule	Ratio = (C2 – M):(M – C1)
Quantity Replacement Formula	Final Concentration = C[1 – (R/T)]ⁿ

Where:

• C = Initial concentration
• R = Quantity removed
• T = Total quantity
• n = Number of repetitions

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🧾 PYQs (Previous Year Questions)

PYQ 1 – SSC CGL 2022

Q: In what ratio must milk costing ₹30/litre be mixed with milk costing ₹50/litre so that the mixture is worth ₹36/litre?
Solution:

30     50  
   \   /  
    \ /  
    36  
   / \  
 14   6 → Ratio = 7:3

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PYQ 2 – IBPS PO 2021

Q: A 20L mixture contains milk and water in the ratio 3:2. How much water should be added to make the ratio 3:4?
Sol:
Milk = 12L, Water = 8L
Let x be added:
(12)/(8+x) = 3/4 → 48 = 24 + 3x → x = 8 litres

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🧠 10 High-Level MCQs with Detailed Solutions

Q1. A 40L mixture contains acid and water in the ratio 7:3. How much water must be added to make the ratio 1:1?

Sol:
Acid = 28L, Water = 12L
Let x be added:
28 = 12 + x → x = 16L

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Q2. Two types of rice costing ₹20/kg and ₹30/kg are mixed to make a mixture worth ₹28/kg. Find the ratio.

20     30  
   \   /  
    \ /  
    28  
   / \  
 2     8 → Ratio = **1:4**

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Q3. A shopkeeper mixes 20L of milk at ₹25/L with 30L of milk at ₹35/L. Find the cost price per litre.

Sol:
(25×20 + 35×30)/50 = (500 + 1050)/50 = ₹31/L

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Q4. In what ratio must water be mixed with a 60% acid solution to make it 20%?

0% (water)    60%
       \     /
        \   /
         20%
        /   \
      40     20 → Ratio = **2:1 (Water:Acid)**

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Q5. A mixture has milk and water in ratio 5:3. If 16L of water is added, the ratio becomes 5:7. Find original quantity.

Sol:
Let milk = 5x, water = 3x
5x/(3x+16) = 5/7 → 35x = 15x + 80 → x = 4
Total = 8x = 32L

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Q6. How many litres of water must be added to 60L of 25% alcohol solution to make it 20%?

Sol:
Alcohol = 15L
Let x be added: 15/(60+x) = 0.20 → x = 15L

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Q7. What is the mean price of mixing 4 kg of sugar at ₹50 and 6 kg at ₹70?

Sol: (4×50 + 6×70)/10 = (200 + 420)/10 = ₹62/kg

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Q8. If 2 solutions contain 40% and 60% alcohol, in what ratio should they be mixed to make 50%?

40     60  
   \   /  
    \ /  
    50  
   / \  
 10   10 → Ratio = **1:1**

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Q9. A milkman replaces 1L milk from a 10L vessel with water and repeats 3 times. Find final milk quantity.

Sol:
Milk left = 10×(1 – 1/10)³ = 10×(729/1000) = 7.29L

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Q10. A 50L mixture has alcohol and water in ratio 3:2. How much water must be added to make it 1:1?

Sol:
Alcohol = 30L, Water = 20L
Let x be added:
30 = 20 + x → x = 10L

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📥 Download Mixture and Alligation PDF Free from GovernmentAdda.com

The PDF includes:

• 🔥 100+ Chapter-Wise MCQs
• 🧮 Formula Sheets
• 📝 SSC, IBPS, CAT PYQs
• 🖊️ Practice Sets with Solutions
• 🧠 Trick-Based Problems for Faster Solving

📥 Click Here to Download the PDF – GovernmentAdda.com

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🤔 Frequently Asked Questions (FAQs)

Q1. Is the Mixture and Alligation PDF really free?
✅ Yes, available for free on GovernmentAdda.com.

Q2. Is this PDF useful for SSC CGL Tier 2 and CAT?
✅ Yes, includes advanced-level sets for both.

Q3. Are shortcut tricks and formulas included?
✅ Yes, each type of question includes tricks and formulas.

Q4. Are solutions given step-by-step?
✅ Yes, with formulas, diagrams, and calculation breakdown.

Q5. How many questions are in the PDF?
✅ 100+ MCQs, 30+ PYQs, 20 High-level CAT-style problems.

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🏁 Conclusion

Mixture and Alligation is a game-changing topic that can boost your Quant score significantly. The free PDF by GovernmentAdda.com is your all-in-one resource packed with:

🔹 Concepts
🔹 Tricks
🔹 PYQs
🔹 Practice Sets
🔹 Detailed Solutions

📌 Download it today and get exam-ready!
👉 Download Now from GovernmentAdda.com

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