Mixture and Alligation: Concept
A mixture, as the name implies, is the combination of two or more items, and alligation allows us to determine the ratio in which the ingredients/objects were combined and at what price they are solely profitable or losing money.
To tackle mixture and alligation, one must first understand that alligation is used to calculate the mean value of a mixture when the ratio and amount of materials blended change, as well as to determine the proportion in which the elements are mixed. It may appear difficult, but after the candidate answers questions based on it, the concept becomes apparent.
Important Formulas for Mixture and Alligation
To solve any numerical ability question, candidates must be familiar with a set of formulae for each topic, which makes the process easier and saves time. Here are a few formulas to assist candidates handle mixture and alligation questions more easily:
The basic formula for calculating the ratio in which the materials are blended is
It is also known as the rule of alligation and can be expressed as
Tips & Tricks for Solving Questions
Time management is critical in government exams, and students cannot afford to waste too much time answering any of the questions. As a result, a few basic methods and ideas will be useful for applicants to easily solve the mixture & alligation questions:
 The rule of alligation can also be used to handle questions related to partnerships, time, work, and wages.
Read a question and putting the values in the alligation rule described above to solve it.  Questions from this area may sound a little tough, but they are easy to solve after a candidate becomes familiar with the concept and the important formulas utilized.
 Using the alligation rule, you may determine not only the ratio between the quantities of two elements, but also the rate at which the object can be sold.
 Any tip will be effective only if a candidate spends quality time practicing combination and alligation problems and applying the alligation rule to solve question’s.
Practice Quizzes
Mixture and Alligation Quiz 1 – Coming Soon 
Mixture and Alligation Quiz 2 – Coming Soon  Mixture and Alligation Quiz 3 – Coming Soon 
Sample Questions on Mixture and Alligation
Q1.There are two types of sugar. One is priced at Rs 62 per kg and the other is priced at Rs 72 per kg. If the two types are mixed together, the price of new mixture will be Rs 64.50 per kg. Find the ratio of the two types of sugar in this new mixture.
 2:5
 3:1
 6:7
 3:2
 None
Explanation:
Cost Price of 1kg of Type 1 sugar = 6200 p.
Cost Price of 1kg of Type 2 sugar = 7200 p.
Mean Price of 1 kg of mixture = 6450 p.
According to the Rule of Alligation,
(Quantity of Cheaper):(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper)
Therefore, the required ratio = (72006450):(64506200) = 750:250 = 3:1.
Q2. A certain quantity of water is mixed with milk priced at Rs 12 per litre. The price of mixture is Rs 8 per litre. Find out the ratio of water and milk in the new mixture.
 3:2
 1:2
 5:2
 2:1
 None of these
Explanation:
Cost Price of 1 litre of water = Rs 0.
Cost Price of 1 litre of milk = Rs 12.
Mean Price of Mixture = Rs 8.
According to the Rule of Alligation,
(Quantity of Cheaper) :(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper)
Therefore, Water : Milk = (128):(80) = 4:8 = 1:2.
Q3. A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo? In the zoo, each horse had four legs and each pigeon had two legs.
 40
 30
 50
 60
 None of these
Explanation:
Let the number of horses = x
Then the number of pigeons = 80 – x.
Each pigeon has 2 legs and each horse has 4 legs.
Therefore, total number of legs = 4x + 2(80x) = 260
4x + 160 – 2x = 260
2x = 100
x = 50.
Q4. An alloy contains a mixture of Zinc, Copper and Iron in the ratio of 4 : 5 : 7. If 24 kg of mixture is taken out and 5 kg of Zinc and 12 kg of Iron is mixed in the alloy. In the resultant mixture quantity of Iron is 26 kg more than Copper, then what is total quantity of initial mixtures?
 106 kg
 112 kg
 121 kg
 136 kg
 none of these
Explanation:
Let after 24 kg of alloy is taken out, the quantity of Zinc, Copper, and Iron be 4x, 5x and 7x kg respectively.
According to question
(7x + 12) – 5x = 26
Therefore, x = 7
∴ Total quantity of initial alloy = 24 + (4x + 5x + 7x) = 24 + 16 × 7= 136 kg.
Q5. A vessel of 80 l is filled with milk and water in parts separately. 75% of milk and 25% of water is taken out of the vessel. It is found that the vessel is vacated by 60%. Find the initial quantity of water.
 24 litres
 27 litres
 32 litres
 36 litres
 40 litres
Explanation:
Let the initial volume of water be ‘w’ litres and the volume of milk = ‘m’ litres
m + w = 80
On removing 75% of milk and 25% of water from the vessel,
0.25m + 0.75w = 80 * 0.4 = 32
= m + 3w = 128
Using the pairs of equations, m = 56, w = 24
Q6. Two vessels A and B contain mixtures of milk and water in the ratios 3 : 7 and 4 : 1 respectively. In a third vessel C, in what ratio should quantities of mixture be taken from vessels A and B are mixed to form a mixture in which ratio of milk and water is 7 : 9?
 3 : 5
 7 : 8
 11 : 9
 11 : 28
 None of these
Explanation:
Using the rule of Alligation, we get
= A : B = 29 : 11
Q7. A mixture of milk and water in a jar contains 29 Liters milk and 9 Liters water. To this mixture, Y Liters milk and Y Liters water are added. If 60% of the new mixture is 36 L, then find the value of Y.
 7 Litres
 11 Litres
 13 Litres
 15 Litres
 None of these
Explanation:
According to the question,
60% of new mixture = 36 L
100% of new mixture = (36/60) × 100 = 60 L
i.e., 29 + 9 + Y + Y = 60
⇒ Y = 22/2 = 11 L
Q8. A mixture of milk and water containing 40 liters of water and y liters of milk. If 50 liters milk is added to the mixture. Then the ratio of milk and water in the resultant mixture become 3:2. Then find the value of y?
 5 liters
 15 liters
 25 liters
 10 liters
 20 liters
Explanation:
The questions above will help you understand how to answer Mixture and alligation questions, as well as the kind of questions that may be asked about this topic.
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