Mixture & Alligation
SSC GD Exam Preparation - Quantitative Aptitude
Mixture & Alligation deals with mixing different quantities and finding ratios, concentrations, and prices of mixtures.
🔹 1. What is Mixture?
A mixture is formed when two or more quantities are mixed together, such as:
- • Two liquids
- • Two types of rice
- • Two types of milk
- • Water added to milk
- • Alcohol-water solution
- • Different priced items
🔹 2. Types of Mixture Problems
(A) Mixing Two Quantities
Two items of different values (price, concentration, ratio) are mixed.
(B) Replacement Problem
Some quantity is removed and replaced with another.
(C) Mean Price or Mean Concentration
Average value of the mixture.
🔹 3. Alligation Rule (The Shortcut Method)
Alligation is used to find ratio in which two items are mixed.
Formula Setup (Alligation Cross Method):
Cheaper | C
Mean | M
Dearer | D
Ratio of quantities = (D - M) : (M - C)
🔹 4. Example (Basic Alligation)
Mix milk at ₹40/litre with milk at ₹60/litre to get mixture of ₹50/litre.
C = 40, M = 50, D = 60
Ratio = (60 - 50) : (50 - 40) = 10 : 10 = 1 : 1
🔹 5. Replacement Formula
If a vessel contains Q litres, and x litres is removed and replaced each time:
Remaining quantity after n operations = Q × (1 - x/Q)ⁿ
Amount removed = Q - Q × (1 - x/Q)ⁿ
🔹 6. Important Concepts
(A) Pure Milk + Water Problems
Water's cost = 0. Milk's cost = positive value. Use alligation directly.
(B) Concentration Problems
Use percentage as cost. Example: 20% acid vs 50% acid → mean 30% acid.
(C) Price Problems
Cost price values are used in alligation calculations.
🧠 15 Practice Questions (With Answers)
Test your mixture & alligation concepts with these SSC GD level practice questions. Click on "View Answer" to check your understanding.
Q1. In what ratio must 20% acid solution be mixed with 50% acid solution to get 30% acid?
View Answer
(50−30):(30−20) = 20 : 10 = 2 : 1
Q2. Mix sugar costing ₹40/kg and ₹60/kg to get mixture of ₹50/kg. Ratio?
View Answer
1 : 1
Q3. Mix rice costing ₹30/kg and ₹45/kg to get mixture worth ₹36/kg.
View Answer
(45−36):(36−30) = 9 : 6 = 3 : 2
Q4. In a mixture of 60 L milk & water, milk is 75%. Find water.
View Answer
Milk = 75% of 60 = 45 L, Water = 15 L
Q5. How much water must be added to 40 L of milk to make it 80% milk?
View Answer
Milk = 40 L, Let total = T, 40 = 80% of T → T = 50 L, Water = 50 − 40 = 10 L
Q6. A 30 L mixture contains 20% alcohol. How much pure alcohol must be added to make it 40%?
View Answer
Alcohol initially = 6 L, Let x be added: (6 + x) = 0.40(30 + x), Solve → x = 10 L
Q7. A mixture contains milk & water in ratio 7 : 3. What % is water?
View Answer
Water % = 3/(7+3) × 100 = 30%
Q8. A vessel has 40 L mixture (milk : water = 3 : 1). 10 L is removed & replaced with water. Find new ratio.
View Answer
Milk = 30 L, Water = 10 L, After removing 10 L: Milk removed = 7.5 L → left = 22.5 L, Water removed = 2.5 L → left = 7.5 L, Add 10 L water → water = 17.5 L, Ratio = 22.5 : 17.5 = 9 : 7
Q9. Two mixtures: A has 30% acid, B has 70% acid. What ratio to get 50%?
View Answer
(70−50):(50−30) = 20 : 20 = 1 : 1
Q10. A shopkeeper mixes ghee costing 400/kg with cheaper ghee costing 300/kg to get mixture worth 360/kg.
View Answer
(400−360):(360−300) = 40 : 60 = 2 : 3
Q11. A mixture has 25% water. After adding 5 L of water, it becomes 40 L total. Find original water.
View Answer
Water now = 5 + original water, Water % = 25%, Solve: (original water + 5) = 0.25 × 40 = 10, Original water = 5 L
Q12. 80 L mixture (milk : water = 5 : 3). Find milk.
View Answer
Total ratio = 8, Milk = 5/8 × 80 = 50 L
Q13. Mix 70% alcohol with water (0%) to get 35% alcohol. Ratio?
View Answer
(35−0):(70−35) = 35 : 35 = 1 : 1
Q14. Vessel contains 100 L pure milk. Each time 10 L is removed & replaced with water, repeated 3 times. Find milk left.
View Answer
Milk left = 100 × (1 − 10/100)³ = 100 × (0.9)³ = 100 × 0.729 = 72.9 L
Q15. A mixture of alcohol & water has 2 : 5 ratio. Find alcohol %.
View Answer
Alcohol % = 2/7 × 100 = 28.57%
✅ SSC GD Exam Strategy
🟢 Practice alligation cross method for quick ratio calculations
🟢 Master replacement formula for removal-addition problems
🟢 Learn to handle percentage concentration scenarios
🟢 Practice price mixture problems - common in SSC GD
🟢 Time yourself - aim for 45-60 seconds per mixture question
You've completed Mixture & Alligation Concepts!
SSC GD Tip: Mixture & Alligation is a high-scoring topic in the quantitative section. Focus on mastering the alligation rule for different scenarios - price mixtures, concentration problems, and replacement cases. Remember to always set up the alligation cross correctly, handle percentage concentrations accurately, and practice the replacement formula for repeated operations. Regular practice with previous year SSC GD questions will build your speed and accuracy in solving mixture problems quickly.
Master Mixture & Alligation for SSC GD Exam!
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