Mixture and Alligation

We need to combine some ingredients in order to make something even in our daily life. We need to prepare mixtures for an activity as small as making tea to as big as manufacturing metals. So let us see what exactly the mixtures are.

I’ll make sure to mix two or more components in a fixed proportion. These proportions can be studied with the help of alligation. Alligation is the formula to find through the ratio of ingredients in a mixture. Alligation helps us find profit and loss after selling the mixtures. Shortcut methods are used to solve the questions of mixtures and allegations.

Mixtures and Alligations

Mixtures are combinations of ingredients, while the location is the ratio in which base ingredients are combined.

For example, lemonade is a mixture, and the ratios of quantities of water, sugar, and lemon with each other are alligations.

The sums on mixtures and alligation appear in a lot of examinations, such as the CMAT. 

The mixtures and alligations questions might appear to be tricky at first, but if you know the mixture and alligations formulas and a few shortcuts, mixture and alligation questions are a great way to earn quick and easy marks.

Mixtures

Mixtures are a combination of two or more ingredients. There are two types of mixtures based on what their constituents are.

The mixtures are of the following two types:

Simple Mixtures: 

In simple mixtures, two or more different components are combined.

The sums based on simple mixtures are pretty straightforward and easy to solve.

For example, 

Alloys are mixtures of two or more metals. Alloys are simple mixtures.

Complex Mixtures:

In complex mixtures, the two or more components that are combined are mixtures themselves as well.

Hence, more ratios need to be calculated while solving the sum of complex mixtures.

When two metal alloys made from a combination of different elements are mixed together, then it leads to the formation of a complex mixture.

Alligation

Alligation Is a way of solving problems related to the ratios of ingredients in mixtures.

There are two types of alligation:

Alligation Medial:

In alligation medial, the quantity of the ingredients is given, and we need to find the quantity of the mixture.

Alligation medial is basically finding a weighted mean.

In weighted mean, each quantity is associated with the particular weight.

For example,

Suppose you combine milk from different brands—1/2 from packet A, 1/4 from packet B, and 1/4 from packet C.

Packet A contains 120 grams of water per litre of milk packet B contains 100 grams of water per litter

Packet C contains 150 grams of water per litre

Find the total amount of water in the mixture of milk.

By using the concept of weighted average,

the amount of water in the mixture of milk will be:

= (1/2) × 120 + (1/4) × 100 + (1/4) × 150

= 122.5

Hence, the total amount of water in the milk mixture is 122.5 grams.

Alligation Alternate:

In alligation alternate, the quantity of the mixture required is given, and we need to find how much quantity of each ingredient will be required to make that much quantity of mixture.

Mixture and alligation questions based on Alligation alternate are much more complex than the alligation medial.

Mixture and Alligation Formulas

You can solve mixture and alligation questions by using any formulas.

However, the basic formulas and rules of alligation will be making cancellations easier and quicker.

The general formula to find the ratio of ingredients in the mixture is:

(Quantity of cheaper/ Quantity of dearer) = ((Cost price of Dearer- Mean price) / (Mean price – cost price of the cheaper))

This is also known as the rule of alligation or the criss-cross method.

Tricks for Mixture and Alligation questions

The rule of alligation is very helpful in solving questions based on mixture and alligation, partnerships, time and work, etc.

Once you read the question, refer to the rule of alligation and determine which quantities represent which part of the alligation rule.

Once You have identified the quantities, draw the criss-cross and place the quantities in the appropriate area of the criss-cross.

Let us solve a few mixtures and alligation questions by applying the formulas and tricks that we just learned.

Question: 30 kg or Basmati rice of price Rs 40/kg is accidentally mixed with the 45kg of normal rice of price Rs 30/kg. Find the price at which the shopkeeper needs to sell this mixture.

By the alligation law, we orange that about you and quantities in the following format.

40             30

         X        

30              45

Now, (30-X): (X -40) = 30:45 = 2:3

90- 3X = 2X -80

5X = 170

therefore, X = 34.

Therefore, the shopkeeper needs to sell a mixture at a price of 34/kg.

Use the above-given formulas to solve mixture and alligation sums.

Conclusion

Mixture and alligation are important chapters as it appears in many competitive exams like CLAT. The mixture is the mixing of two or more ingredients. A mixture can be a simple mixture, or it can be a complex mixture.

Alligation is the rule of mathematical concept which is used to identify the ratio in which the ingredients of the mixtures are mixed. There are two types of alligation: alligation medial and alligation alternate. The law of alligation or the criss-cross method helps in finding out the ratios in a mixture in a simpler way. It also helps to solve partnership questions.