Mixture and Alligation MCQs test your ability to solve complex problems related to combining different quantities of substances to obtain desired mixtures. These questions are commonly seen in competitive exams like CAT, NMAT, SNAP, XAT, etc. To tackle them efficiently, it is crucial to understand the concepts of proportions, averages, and ratios, enabling you to solve these MCQs within 60 seconds without relying on a calculator.
Multiple Choice Questions
Que 1: What is the initial quantity of the mixture in the vessel (in litres), given that a vessel contains a mixture of Grape, Pineapple, and Banana juices in the respective ratio of 4:6:5, 15 litres of this mixture is taken out, and 8 litres of grape juice and 2 litres of pineapple juice are added to the vessel, resulting in a quantity of grape juice that is 10 litres less than the quantity of pineapple juice?
(a) 120
(b) 150
(c) 105
(d) 135
Solution: (6x+2)-(4x+8)=10
x=8
4x+6x+5x=15x=120 litres
120+15=135 litres
Option (d) is correct.
Que 2: What is the amount of mixture that was taken out from Jar A (in litres), given that in Jar A, 180 litres of milk was mixed with 36 litres of water, and some of this mixture was transferred to Jar B? After adding 6 litres of water to the mixture in Jar B, the ratio between milk and water in Jar B was 5:2?
(a) 24
(b) 54
(c) 30
(d) 36
Solution: Jar A⇒Milk : Water= 180: 36= 5 :1
Jar B⇒Milk : Water=5x :x+6= 5:2
x=6
The amount of mixture that was taken out from Jar A= 6x=36 litres
Option (d) is correct.
Que 3: What is the quantity of rice of cost Rs. 24 per kg used in the mixture, if a farmer mixes two varieties of rice priced at Rs. 36 per kg and Rs. 24 per kg in the ratio of 1:2, respectively. The farmer sold the mixture for Rs. 2100, earning a profit of 25%.
(a) 20 kg
(b) 30 kg
(c) 40 kg
(d) 50 kg
Solution: Let the average price= x
x-24: 36-x=1:2
x=28
CP: SP= 4:5
4 unit=28
5 unit=35 per kg
Total mixture= 2100/35=60 kg
The quantity of rice of cost Rs. 24 per kg=60×2/3= 40 kg
Option (c) is correct.
Que 4: What proportion of the volume of vessel C should be the volume of water added, so that the ratio of milk and water in vessel C becomes 1:1? Given that vessel A and vessel B, both of equal volume, contain milk and water in the ratio of 3:2 and 2:1, respectively, to their brim. Additionally, two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C, and the resulting solution in vessel C occupies 40% of its capacity.
(a) 21/125
(b) 2/25
(c) 14/125
(d) 4/25
Solution: Milk : Water
A⇒ (3:2)×3=9:6
B⇒ (2:1)×5=10:5
2 litres of A⇒ Milk : Water=2×9/15: 2×6/15= 1.2: 0.8
3 litres of B⇒ Milk : Water=3×10/15: 3×5/15= 2:1
In the vessel C⇒ Milk: Water= 3.2: 1.8
40% of the vessel C= 5 litres
Capacity of vessel C= 12.5 litres
Required water= 3.2-1.8=1.4 litres
Option (c) is correct.
Que 5: How many litres of mixture were initially in the tank, given that Royal Asian Paints mixes Pink and White in the ratio of 4:5 in a tank. After mixing, the company realises that the resultant shade has less Pink, so they remove 18 litres of the mixture and add an equivalent quantity of Pink. As a result, the shade obtained has Pink and White in the inverse ratio.
(a) 72 litres
(b) 90 litres
(c) 80 litres
(d) 95 litres
Solution: Initial⇒ 4:5
Final⇒ 5:4
Decrement in water=Decrement in mixture= 1/5th= 18 litres
Total mixture= 18×5= 90 litres
Option (b) is correct.
Que 6: What is the quantity of 60% pure milk that the milkman mixed in order to make a profit of 33.33% by selling a mixture of 45 litres of 80% pure milk and 60% pure milk at the cost price of pure milk?
(a) 16 litres
(b) 20 litres
(c) 12 litres
(d) 15 litres
Solution: When we say that there is a 33.33% profit by selling at the cost price, it means that the milk and water ratio in the mixture is 3:1 (75% pure milk)
x: 45= (80%-75%): (75%-60%)=1:3
x=15 litres
Option (d) is correct.
Que 7: In order to form a final mixture where the percentage of water is 36.8%, what is the ratio at which the two given mixtures of alcohol and water, one containing 48 L with 32 L of alcohol and the other containing 32 L with 20 L of alcohol, need to be mixed together?
(a) 2:5
(b) 21:104
(c) 9:112
(d) 15:91
Solution: Percentage of water in 1st container= 1600/48=(100/3)%
Percentage of water in 2nd container= 1200/32=37.5%
Final concentration of water= 36.8%
Required ratio= (37.5-36.8): (36.8- 100/3)=21: 104
Option (b) is correct.
Que 8: What is the percentage of aqua in the resultant mixture if a vessel initially contains 100 litres of a mixture of acid and aqua in the ratio of 4:1, 30% of the mixture is taken out, 2 litres of aqua is added, another 25% of the mixture is taken out, and 3 litres of acid is added?
(a) 27.25%
(b) 25.12%
(c) 21.05%
(d) 17.22%
Solution: Acid : Aqua
80 litre : 20 litre
56: 14 (30% removed)
56: 16 (+2 litre aqua)
42: 12 (25% removed)
45: 12 (+3 litre acid)
Final ratio= 15: 4
Percentage of aqua= 400/19=21.05%
Option (c) is correct.
Que 9: How much petrol is currently contained in the drum if it initially had 60 litres of petrol, and 6 litres of petrol were taken out and replaced with kerosene, repeating this process two more times?
(a) 40.84 litres
(b) 41.65 litres
(c) 42.94 litres
(d) 43.74 litres
Solution: Each time, 10% of the petrol was removed from the drum.
10^3:9^3=1000:729
1000 unit=60 litres
729 unit= 43.74 litres
Option (d) is correct.
Que 10: Approximately after how long will the drug start depositing at the base if water is evaporated at a rate of 28g/h from a 1kg mixture containing 4% drug, and the maximum amount of drug that can be dissolved into 100g of water is 25g?
(a) 15 h
(b) 23 h
(c) 29 h
(d) 35 h
Solution: Amount of drug= 40g
Required water= 40×4=160g
1000-(160+40)=800g
800/28≈29 h
Option (c) is correct.
Que 11: How many gallons of juice are removed each time if a juice seller wants to make a juice cocktail by mixing cranberry juice and apple juice? The seller starts with a can full of cranberry juice, and a certain quantity of cranberry juice is taken out and replaced with the same quantity of apple juice. This process is repeated, and after the second replacement, the mixture contains 19% apple juice. Given that the volume of the can is 20 gallons.
(a) 5 gallons
(b) 4 gallons
(c) 3 gallons
(d) 2 gallons
Solution: Cranberry Juice: 100 unit⇒81 unit (After two replacements)
10^2: 9^2.
This means that every time 10% of the mixture is replaced.
10% of 20 gallons= 2
Option (d) is correct.
Que 12: How much of the bottle did the butler steal if he took wine from a bottle of Sherry containing 18% spirit and replaced it with wine containing only 8% spirit, resulting in the bottle having a spirit strength of 14%?
(a) 1/4
(b) 2/5
(c) 3/5
(d) 3/4
Solution: Apply Alligation method
The ratio between the 18% spirit and the 8% spirit is 3:2
In this mixture, 2 units are replaced out of a total of 5 units.
Option (b) is correct.
Que 13: What is the ratio of milk to water in the resultant mixture when three solutions, with milk and water ratios of (2:3), (3:1), and (4:5) respectively, are mixed in the ratio of 2:3:4?
(a) 219: 341
(b) 531: 622
(c) 640: 729
(d) 869: 751
Solution: 2:3⇒5 unit×36= 72:108
3:1⇒4 unit×45= 135:45
4:5⇒9 unit×20= 80:100
(72:108)×2=144:216
(135:45)×3=405:135
(80:100)×4=320:400
Final ratio= 144+405+320: 216+135+400=869: 751
Option (d) is correct.
Que 14: How much quantity of pulses is sold at a 14% profit and how much quantity is sold at a 6% loss if a trader has 50 kg of pulses, and the overall loss incurred is 4%?
(a) 5 kg, 45 kg
(b) 15 kg, 35 kg
(c) 10 kg, 40 kg
(d) None
Solution: -4-(-6): 14-(-4)=2:18=1:9
Option (a) is correct.
Que 15: What is the original volume of the solution if a vessel initially contains milk and water in the ratio of 3:2, the volume of the contents is increased by 50% by adding water, 30 litres of the resultant solution is withdrawn and replaced with water, and the final ratio of milk to water in the solution is 3:7?
(a) 80 L
(b) 65 L
(c) 75 L
(d) 60 L
Solution: Milk: Water= 3: 2
add water
M: W= 3: 2+2.5= 2:3⇒ 5 unit
After replacement
M:W= 3:7⇒ 10 unit
(2:3)×2=4:6
3:7
1/4th of the mixture has been replaced
1/4th= 30 litres
Total= 120 litres
1.5 times= 120 litres
Initial quantity= 80 litres
Option (a) is correct.