SSC CGL Mixture & Alligation MCQs with detailed solutions, shortcut tricks, and Tier II level questions to improve calculation speed, accuracy, and exam preparation.
SSC CGL Mixture & Alligation MCQs
1. A mixture contains milk and water in the ratio 7 : 3. If 20 liters of water is added to the mixture, the ratio becomes 7 : 5. What was the original quantity of the mixture?
A. 100 litres B. 120 litres
C. 140 litres D. 160 litres
Correct Answer: A. 100 litres
Explanation:
Let the original quantities of milk and water be 7x and 3x.
After adding 20 liters of water:
35x = 21x + 140
35x = 21x + 140
14x = 140
⇒ x = 10
Original mixture: 7x+3x=10x
10 × 10 = 100
2. A vessel contains 60 liters of a mixture of milk and water in the ratio 2 : 1. How much water should be added to make the ratio 1 : 2?
A. 45 litres B. 50 litres
C. 60 litres D. 75 litres
Correct Answer: C. 60 litres
Explanation:
Milk = 60 × (2/3) = 40
Water = 20 litres.
Let x litres of water be added.
80 = 20 + x
x = 60
3. A 40-liter mixture contains milk and water in the ratio 3 : 1. How much mixture should be replaced by water so that the ratio becomes 1 : 1?
A. 13⅓ litres B. 14⅓ litres
C. 12⅓ litres D. 23⅓ litres
Correct Answer: A. 13⅓ litres
Explanation:
Initial milk = 30 litres, water = 10 litres.
Suppose x litres of mixture are removed. Since the mixture is in the ratio 3 : 1:
Milk removed = 3x/4
Water removed = x/4.
Remaining milk = 30 – 3x/4
Remaining water 10 – x/4
After adding x litres of water:
10 – x/4 + x = 30 – 3x/4
10 + 3x/4 = 30 – 3x/4
20 = 3x/2
x = 40/3 = 13⅓
SSC CGL Mixture & Alligation MCQs
4. In what ratio should a 30% alcohol solution be mixed with a 70% alcohol solution to obtain a 50% alcohol solution?
A. 1 : 1 B. 2 : 1
C. 1 : 2 D. 3 : 2
Correct Answer: A. 1 : 1
Explanation:
Using alligation:
30% 70%
Mean = 50%.
Ratio: (70 – 50): (50 – 30) = 20 : 20 = 1:1
5. A merchant mixes rice costing ₹ 40 per kg with rice costing ₹ 60 per kg and sells the mixture at ₹ 66 per kg, making a profit of 20%. What is the ratio of cheaper rice to costlier rice?
A. 1 : 3 B. 2 : 1
C. 3 : 2 D. 2 : 3
Correct Answer: A. 1 : 3
Explanation:
Selling price = ₹ 66.
Profit = 20%.
Therefore, mixture cost price:
CP= 
= 55
Mean = 55.
Ratio: (60 – 55) : (55 – 40) = 5 : 15 = 1 : 3
6. A container has 80 litres of milk. 20 litres are removed and replaced with water. This process is repeated once more. How much milk remains?
A. 40 litres B. 45 litres
C. 48 litres D. 50 litres
Correct Answer: C. 45 litres
Explanation:
The fraction retained each time is:
1 – 20/80 = 3/4
After two operations:
80 (3/4)2 = 80 (9/16)
= 45
∴ 45 litres of milk remain.
7. A 60-litre mixture contains milk and water in the ratio 5 : 1. How much mixture must be removed and replaced with water to make the ratio 3 : 1?
- 6 litres B. 10 litres
- 12 litres D. 15 litres
Correct Answer: A. 6 litres
Explanation:
Initial milk:
60 × 5/6 = 50
Let x litres of mixture be replaced.
Milk removed: (5/6)x
Final milk: 50 – (5/6)x
Final total mixture remains 60 litres.
For a 3 : 1 ratio, milk should be:
60 × 3/4 = 45
Therefore:
50– (5/6)x = 45
(5/6) x = 5
x = 6
8. Two varieties of tea costing ₹240 per kg and ₹300 per kg are mixed with a third variety costing ₹360 per kg. If the quantities of the first and second varieties are equal and the average cost is₹300 per kg, what is the ratio of the quantity of the third variety to either of the first two?
A. 1 : 1 B. 2 : 1
C. 1 : 2 D. 3 : 2
Correct Answer: A. 1 : 1
Explanation:
Lthe quantitiesies of the first and second varieties be x each and the third be y.
= 300
540x + 360y = 600x + 300y
60y = 60x
y = x
y:x=1:1
SSC CGL Mixture & Alligation MCQs
9. A solution contains 25% acid. How much pure acid should be added to 80 litres of the solution to make the acid concentration 40%?
A. 15 litres B. 20 litres
C. 25 litres D. 30 litres
Correct Answer: B. 20 litres
Explanation:
Initial acid:
80 × 25% = 20
Let x litres of pure acid be added.
= 40%
20 + x = 32 + 0.4x
0.6x =12
x = 20
10. A 50-litre mixture contains milk and water in the ratio 4 : 1. How much water must be added so that water becomes 30% of the final mixture?
Corrected Options:
A. 5 litres B. 7⅐ litres
C. 10 litres D. 12½ litres
Correct Answer: B. 7⅐ litres
Explanation:
Initial milk = 40 litres.
Initial water = 10 litres.
Let x litres water be added.
Final quantity:
50+x
Water:
10+x
Given:
= 30%
10 + x = 15 + 0.3x
0.7x = 5
x= 50/7=7⅐
11. A vessel contains 90 litres of a mixture of milk and water in the ratio 7 : 2. How much mixture should be removed and replaced with water so that the ratio becomes 7 : 3?
A. 9 litres B. 10 litres
C. 12 litres D. 15 litres
Correct Answer: A. 9 litres
Explanation:
Initial milk:
90 × 7/9=70
Let x litres be replaced.
Milk removed:
(7/9)x
Final milk:
70 – (7/9)x
For a 7 : 3 ratio in 90 litres, milk must be:
90 × 7/10=63
Therefore:
70– (7/9)x = 63
(7/9)x =7
x = 9
SSC CGL Mixture & Alligation MCQs
12. A mixture of 20 litres contains alcohol and water in the ratio 3 : 2. How much water should be added to make the ratio 1 : 1?
A. 2 litres B. 4 litres
C. 6 litres D. 8 litres
Correct Answer: B. 4 litres
Explanation:
Alcohol = 12 litres.
Water = 8 litres.
For 1 : 1 ratio, water must also be 12 litres.
Required water:
12 – 8 = 4
13. A shopkeeper mixes two varieties of sugar costing₹32/kg and₹44/kg in the ratio 3 : 2. If he sells the mixture at a profit of 25%, what is the selling price per kg?
A.₹44.00 B.₹46.00
C.₹47.50 D.₹48.00
Correct Answer: B.₹46.00
Explanation:
Mixture CP:
Selling price at 25% profit:
36.8 × 1.25 = 46
14. In what ratio should water be mixed with milk costing₹72 per litre so that, by selling the resulting mixture at₹72 per litre, a profit of 20% is obtained?
A. 1 : 4 B. 1 : 5
C. 1 : 6 D. 2 : 5
Correct Answer: B. 1 : 5
Explanation:
If SP = ₹72 and profit = 20%
CP = 72/1.2 = 60
The mixture contains milk costing ₹72 and water costing ₹0.
Using alligation: 0 72
Mean = 60.
Water : Milk:
(72–60):(60–0)=12:60=1:5
15. A 100-liter mixture contains 60% milk. How much mixture should be removed and replaced with pure milk to make the milk content 68%?
A. 15 litres B. 20 litres
C. 25 litres D. 30 litres
Correct Answer: B. 20 litres
Explanation:
Initial milk = 60 litres.
Let x litres of mixture be removed.
Milk removed = 60% of x = 0.6x.
Pure milk added = x.
Final milk:
60 – 0.6x + x = 60 + 0.4x
Required milk:
68% of 100 = 68
60 + 0.4x = 68
x = 20
16. A mixture contains 40 litres of milk and 10 litres of water. If 10 litres of the mixture is removed and replaced with water, what is the new ratio of milk to water?
A. 16 : 9 B. 3 : 2+
C. 2 : 1 D. 5 : 3
Correct Answer: A. 16 : 9
Correct Answer: A. 3 : 2
Explanation:
Initial ratio = 40 : 10 = 4 : 1.
In 10 litres removed:
Milk removed = 8 litres.
Water removed = 2 litres.
Remaining:
Milk = 32 litres.
Water = 8 litres.
Add 10 litres water:
Water = 18 litres.
New ratio:
32:18=16:9
SSC CGL Mixture & Alligation MCQs
17. A 30-liter solution contains 40% acid. How much water must be evaporated to increase the acid concentration to 50%?
A. 5 litres B. 6 litres
C. 8 litres D. 10 litres
Correct Answer: A. 6 litres
Explanation:
Acid remains unchanged:
30 × 40%=12
At 50% concentration, total solution should be:
12/0.5=24
Water evaporated:
30–24=6
18. A vessel contains 72 litres of a mixture of milk and water in the ratio 5 : 3. How much water should be added to make the ratio 5 : 4?
A. 6 litres B. 9 litres
C. 12 litres D. 15 litres
Correct Answer: B. 9 litres
Explanation:
Milk:
72 × (5/8)=45
Water = 27 litres.
For ratio 5 : 4, if milk = 45, water must be:
45×(4/5) =36
Additional water:
36 – 27=9
19. Three varieties of rice costing ₹20, ₹30, and ₹50 per kg are mixed in the ratio 2 : 3 : 5. What is the average cost per kg of the mixture?
A.₹35 B.₹36
C.₹38 D.₹40
Correct Answer: C.₹38
Explanation:
20. A container contains 64 litres of pure milk. In each operation, 16 litres of the mixture are removed and replaced with water. How many litres of milk remain after three such operations?
A. 24 litres B. 27 litres
C.30 litres D. 32 litres
Correct Answer: B. 27 litres
Explanation:
Fraction of milk retained in each operation:
1–(16/64) =3/4
After three operations:
64 × (3/4)3
= 64 × (27/64) = 27
SSC CGL Quantitative Aptitude Topics
- Number System
- Decimals
- Fractions
- Percentages
- Ratio & proportion
- Square roots
- Averages
- Interest (simple & compound)
- Profit & loss
- Discount
- Partnerships
- Mixture & Alligation
- Time & speed & distance
- Time & work.
- Advanced math includes basic algebraic identities
- Elementary surds
- Graphs of linear equations
- Triangles
- Circles
- Regular polygons, right prisms, cones, cylinders, spheres
- Trigonometry.
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