Mixture and Alligation Tricks

Mixture and Alligation Tricks questions are gaining importance in competitive exams be it for IBPS Clerk, PO, RRB, SO, or SBI Clerk or PO. The number of questions and the complexity of questions vary from exam to exam every year.

Mixture and Alligation Tricks are complex in nature and require an understanding of Math Tables, Percentage Calculation, and Ratio and Proportion other types of Arithmetic and Geometric Series are given in this article.

In this article, we have solved Examples of Mixture and Alligation Tricks and Practice Question on Mixture and Alligation Tricks.

Nowadays, questions in exams are mixed with other mathematical concepts and it requires practice and a deep understanding of basic concepts along with quickly identifying numbers.

What are Mixture and Allegation?

Mixture and Alligation is a rule which is applied when we have to find a ratio in which two or more quantities at any given price of each quantity to get a mixture of desired price and quantity.

For Example, There are two types of rice ‘A‘ of price 10 rs per kg and ‘B‘ of price 15 rs per kg. In which quantity ratio both rice should be mixed so that price of the mixture is 13 rs per kg?

Solution: Let A price be 10 and B price be 15 and the desired price (M) be 13. Now we need to find a ratio in which quantity should be mixed so that the mixture price will be 13.
=> ‘A’ quantity will be the difference between ‘B’ price and ‘M’ price.
Hence ‘A’ quantity will be 15 – 13 = 2 Kg.
=> ‘B’ quantity will be the difference between ‘M’ price and ‘A’ price.
Hence ‘B’ quantity will be 13 – 10 = 3 Kg.

Desired Ratio in which mixture of A and B type rice will be 2:3

What is Mean Price?

Mean price is the price per unit of mixture quantity which was formed by mixture and alligation of two or more same type of item.

How to find Mean Price?

When we create any mixture and alligation of any item of any given price and quantity. New mixture whose mean the price will be calculated as below:

Mean Price = { (A Price x A Quantity) + (B Price x B Quantity) } / (A Quantity + B Quantity)

For Example: Determine the mean price of the mixture that was formed by mixing 3 Kg of 10 rs rice and 2 Kg of 15 rs rice?

Solution: As per the formula of Mean price, when we substitute values we get:
=> MP = { (10 x 3) + (15 x 2) } / (2 + 3)
=> MP = { 30 + 30 } / 5
=> MP = 60 / 5
=>MP = 12 {Means price of Mixture is 12 rs per Kg}

Repeated Dilution

In the mixture and alligation tricks, repeated dilution is also a concept that is solved using different approaches. First, understand What is Repeated Dilution? In repeated dilution, a concentrated liquid is diluted multiple times.

To get amount let of concentrated liquid in container after dilution we use below formula:

Concentrated Liquid = [x{1 – (y/x)}ⁿ]

For Example: A container has 100 liters of milk and from that container, 4 liters of milk are taken out and replaced with water and this process is repeated again, then how much pure milk is left in the container?

Solution: Applying above formula:
x is 100 litres, y is 4 litres and n is 2 (repeated twice). On substituting these values in formula, we’ll get:
=> Pure Milk = [100{1 – (4/100)}²]
=> Pure Milk = [100{1 – (16/10000)}]
=> Pure Milk = [100{(10000 – 16)/10000}]
=> Pure Milk = [(10000 – 16)/100]
=> Pure Milk = [(10000 – 16)/100]
=> Pure Milk = [9984/100]
=> Pure Milk = 99.84

Solved Example by Mixture and Alligation Tricks

Below are the solved example of Mixture and Alligation Tricks:

Example 1: Wheat of A type 18 rs/kg and B type 23 rs/kg and their average value is 20 rs/kg. Find the ratio of the new mixture quantity?

Solution 1: Mean Price is 20,
=> 23 – 20 = 3
=> and 20 – 18 = 2
Desired Ratio of quantity is 3:2.

Example 2: Rice of A type 17 rs/kg and B type 25 rs/kg and their average value is 20 rs/kg. Find the ratio of the new mixture quantity?

Solution 2: Mean Price is 20,
=> 25 – 20 = 5
=> and 20 – 17 = 3
Desired Ratio of quantity is 5:3.

Example 3: Mixture of 30 Kgs of A-type wheat 20 rs/kg and 30 Kgs of B-type wheat 28 rs/kg. Find the mean price?

Solution 3: Applying formula to find Mean Price, we’ll get
=> MP = {(20 x 30) + (30 x 20)} / (20 + 30)
=> MP = {600 + 600} / 50
=> MP = 1200 / 50
=> MP = 24

Example 4: Mixture of 30 Kgs of A-type wheat 15 rs/kg and 20 Kgs of B-type wheat 30 rs/kg. Find the mean price?

Solution 4: Applying formula to find Mean Price, we’ll get
=> MP = {(15 x 30) + (28 x 30)} / (30 + 30)
=> MP = {450 + 840} / 60
=> MP = 1290 / 60
=> MP = 21.5

Example 5: A container of 40 liters of milk. If 4 liters of milk were taken out and replaced by water. This process was repeated further two times. How much pure milk is now in a container?

Solution 5: Applying above formula:
x is 40 litres, y is 4 litres and n is 3 (repeated thrice). On substituting these values in formula, we’ll get:
=> Pure Milk = [40{1 – (4/40)}³]
=> Pure Milk = [40{1 – (64/64000)}]
=> Pure Milk = [40{(64000 – 64)/64000}]
=> Pure Milk = [(64000 – 64)/1600]
=> Pure Milk = [63936/1600]
=> Pure Milk = 39.96

Practice Questions of Mixture and Alligation Tricks

Below are the practice questions of Mixture and Alligation Tricks:

1. A type of wheat is 22 Rs/kg and B type of wheat 30 kgs is mixed to form a mean price of 28 Rs/kg. Find the price of B?
2. A type of wheat of 30 kg cost of 16 Rs and B type of wheat costs 20 Rs is mixed to get a mean price of 17 Rs/kg. Find the quantity of B type?
3. What is the mean price of a mixture of 30 Kg of A-type rice of 40 Rs/kg and 20 Kg of A-type rice of 60 Rs/kg?
4. What is the mean price of a mixture of 50 Kg of A-type rice of 60 Rs/kg and 30 Kg of A-type rice of 45 Rs/kg?
5. If the Mean Price of an 80 Kg mixture was 42 Rs/kg, which was calculated wrong and when realized 10 kg were sold. If the difference between the mean price and the correct mean price was 10 rs. Then find what will be the new mean price?
6. If the Mean Price of a 100 Kg mixture was 60 Rs/kg, which was calculated wrong and when realized 20 kg were sold. If the difference between the mean price and the correct mean price was 8 rs. Then find what will be the new mean price?
7. Find the Ratio of the mixture if 80 Kg of A1 wheat is mixed with 100 Kg of A2 wheat. The price of A1 and A2 is 18 Rs/kg and 22 Rs/kg respectively.
8. Find the Ratio of the mixture if 28 Kg of A1 wheat is mixed with 36 Kg of A2 wheat. The price of A1 and A2 is 12 Rs/kg and 15 Rs/kg respectively.
9. A container has concentrated Alcohol of 50 Litres and if the shopkeeper takes out 5 liters and replaces it with water and repeats this step two more times then what amount of pure alcohol is left?
10. A container having concentrated Acid of 15 Litres and if the shop keeper takes out 3 liters and replaces it with water and repeats this step thrice more times then what amount of pure acid is left?

Final Words

Practicing the above questions for Mixture and Alligation tricks is not the end of your practice, but it’s a start of a new journey to apply logic to Mixture and Alligation tricks solutions with multiple approaches in right and faster way.

For cracking competitive exams one must practice Mixture and Alligation tricks without a calculator is a must. At last, during the exam, if a solution for Mixture and Alligation tricks questions cannot be found easily then mark that question to revisit and move ahead instead of wasting time and energy.