Alligation and Mixture | Concepts, Tips and Tricks

Alligation and Mixture | Concepts, Tips and Tricks

Let us begin with some definitions.

Mixing 2 or more types of quantities gives us a mixture.

These quantities can be expressed as a percentage or a ratio/fraction.

  • Percentage (30% of milk in water)
  • Fraction (A solution of sugar and water such that sugar: water=1:4)


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The allegation is the rule that helps us find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

As Merriam-Webster defines it, Alligation is “A process or rule for the solution of problems concerning the compounding or mixing of ingredients differing in price or quality”.

Now, know these essentials before you mess with allegations and mixtures!

  • The cost price of a unit quantity of the mixture is called the mean price.
  • There are two types of Allegations:


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Allegation Medial: This rule is used to find the quantity of a mixture when the quantity of its ingredients is given.

Allegation Alternate: This rule is used to find the amount of each ingredient needed to make a mixture of a given quantity.

  • HCF & LCM are your primary defences. Master them.
  • In a mixture, you seldom know the amount of 2 components mixed. The proportion of mixing is mentioned in most of the questions. Ratios and proportions constitute your secondary defence.
  • Fight against time before you face the real challenge! Mocks are important irrespective of whether a topic is easy or not. Track the time taken by you to solve questions from this concept.
  • Concept knowledge is more important than learning formulae. Know the concepts well.

Once your defences are strong you are all set to tackle the trickiest of questions shot at you from this topic. However, listed below are some critical formulae which will be crucial in saving time while you appear for competitive exams.

Rather than memorizing the formulas try to understand the concept behind them. It will make your life easier.



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How to tackle the questions?

  • If two components A and B of the price a and b respectively are mixed and the price of the resultant mixture is M (mean price) then the ratio (R) in which ingredients are mixed is given by, the rule of allegation R= (M-b)/ (a-M)
  • Suppose from a container containing a solution, some amount is taken out and replaced with one of the ingredients. Then this process is repeated v times.
  • The Final Amount of Ingredient that is not replaced = Initial Amount x (volume after removal/volume after replacing)v
  • The final ratio of an ingredient not replaced to total = Initial Ration x (volume after removal/volume after replacing)v
  • Suppose a container contains X units of liquid from which Y units are taken out and replaced by water. After n operations, the quantity of pure liquid is [X*(1-(Y/X))n]
  • P gram of ingredient solution has x% ingredient in it. To increase the ingredient content to y% in the solution, the number of ingredients needed to be added= p (b-a)/ (100-b)

 

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Why is it critical in conquering Alligation and Mixtures?

Alligations and Mixtures no doubt can be conquered easily and hence it becomes very strategic for a person trying to clear cut-off or enhance their score to give his 100% in this section. Questions on this topic are also asked regularly in tests from TCS, Cognizant, Infosys, Wipro etc.

Time to Conquer! 

Now that our defences are strong it’s high time that we try to analyze how the questions will be shot at us.

  • 2 liquids in different quantities will be taken and mixed together. One might be asked either to calculate the concentration of the final mixture or the selling price of this mixture.
  • Highly unlikely that every time liquids get a chance even solids can irritate you as much as liquids!
  • 2 Components X & Y are taken (solid or liquid) and mixed. Now you might be asked to calculate the amount of Component X or Y that needs to be added to the mixture to reduce the concentration of Y or X by a certain amount. This is killer! Beware of it as it deceives you most of the time.
  • When it comes to application-based questions the concept or rule of alligations and mixtures can be extended to average speed, average height, interest rates and a lot more. Mathematically “weighted averages” problems are what you are dealing with.

 

Happy Solving!



allegation and mixture concepts tips and tricks

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