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Are there any Tricks to Solving Allegation and Mixture Problems ?

What is Allegation in Mathematics – This is an old and recurring method or practice so to say which is also considered highly practical. They solve mathematical problems here using mixtures of different types of ingredients. We know of two types of Alligation- one is Alligation Medial and other is Alligation Alternate. The first one is used to:

  • Alligation Medial is used for measuring the quantity of a mixture when we already know the quantity of the ingredients.
  • Alligation Alternate- is used to find or measure the amount of each ingredient needed to make the required mixture.

We have two different variation for this Alligation which is that this is nothing but finding the mean. The latter which is Alligation Alternate is the more complex process which is used to make the materials more organised and that they are often described as high and low. We also have something called the Alligation Partial and total and these methods are not common however they are still widely used for chemical analysis or measuring quantities for chemists and pharmacies.

Example for Medial: Suppose we make a drink which has three basic combination. One is Coke which has sugar amount of 100 grams per litre, next is the Pepsi which has the sugar amount of 130 grams per litre. Last one is basic orange drink which has 110 sugar per litre. Now how do we find the amount of sugar in the combined mixture. Thus it is important here to find the wighted average of the combination drink/

Example for Alternate:  Suppose we have to make a cake. Here for a 1 kg cake we need to give some basic ingredients. Now we know that the measurement here is very important. We want to find the amount of these ingredients to form a mixture and thus give us an end product. We have maybe three basic ingredients here to make a cake. We desire maybe a little more cocoa or little more butter cream in the cake and thus we need to divide the total from the sum of the amount of the ingredients each taken.

Rule of Alligation

What is the rule of alligation – so to understand how the formula works and the rules work as well we need to find the meaning and difference of what is the weighted average of the ingredients and also the general rule towards it. Apart from weighted average method we also know the concept of the repeated dilution which is used for this process. This is one of the most simple and effective method used by chemist and pharmacists to illustrate and drive calculation for the measurements of the ingredients. Where we see and check the proportion of any solution which needs to be mixed and thus we come out with a final product. This final product is of a said proportion and concentration. When we use water then it is simply called as Dilution method.

Here we study two mixtures of two or more quantities and these mixtures or ingredients have different cost and selling price. If we find a mixture of one expensive substance and another one cheap substance than what is the result. Here we also need to know about the mean price.

For example- Suppose we buy 10 packets of potato chips each of Rs 15 each. Then in another instance we buy 23 packets of potato chips which is of price 12 each. So now do we take the average of the chips which cost us 15 or 12 Rupees. Thus the concept of weighted average comes here and considered very important to this.

The basic use for Allegation method is that it can help determine the parts of the same product and these parts might have different quantities and also we need to know how much is needed for what to make the final product. Plus we also need to know how many millimetres or maybe grams of products we need to make the final product.

The basic formula for Aligation is: We have to find the mean price which is nothing but the unit quantity of the mixture. That is the one quantity which is less in price and is cheaper. So we have

Cheaper quantity – costly quantity: Mean – C.

How it works as in- Firstly we need to identify the data which is given to us. Next is to convert all the data into smaller units and forms. All the concentration are in volume terms. Then we apply the allegation formula to it.

Learn more: Indefinite Integrals from Class 12 Maths