Mixture and Alligation Shortcuts

Alligation or Mixture's formula

Alligation and Mixture Solved Questions

Friends, today we shall discuss about an important concept for Banking and Other Competitive Exams - Mixture and Alligation. Usually people leave this section because its little confusing. But trust us friends, we will make it easier for you. Lets start with the basics.....


What is mixture?

A Mixture is a solution containing two or more products (we can simply call these products as Elements of the mixture) which bear a certain proportion to each other by quantity. This may be expressed in terms of

• Percentage (ex: 25% of salt in water)
• Fractions (ex: A solution of water and milk such that: water: milk = 5:7)

When you add two mixtures, the respective quantities of these elements of the mixtures get added, thereby affecting the overall contents of the combination. So, the resultant mixture would have " a weighted proportion" of the two elements.

It is presumed that no Chemical Reaction takes place while the tow mixtures are combined. So these are physical mixtures rather than chemical mixtures. (This clarification is for those chemical geniuses who thinks about Evaporation;)

Rule of Alligation

When two or more quantities of different products are mixed together to produce a mixture of a mean value, the ratios of their amounts  are inversely proportional to the differences of their values form the mean value. Please read the above statement. Its the heart of our concept.

Confused? lets read this in simple words....

If the gradients are mixed in a ratio, then 

Quantity of Cheaper/Quantity of Dearer  =  C.P of Dearer - Mean Price/ Mean Price - C.P of Cheaper

We can represent the above Statement as

Then, 

(Cheaper Quantity) : (Dearer Quantity) = (d - m) : (m - c)

• Where can we apply the rule of Mixture and Alligation?

  
  

  You can apply this when you have to find the proportion in which different ingredients of known value are to be mixed to produce a mixture of a given mean value. You can apply this when you have to find the mean value of a mixture when the proportion and value of its ingredients are known.

• What types of questions can I expect from Mixture and Allegation for Exams?

  
  

  Ex. 500 ml solution of water contains 10% of milk. How much pure water needs to be added to this solution in order to get the percentage of milk as 8% ?

  
  

  
  

  Sol: We can solve this problem using two methods. First we shall discuss solving this question using conventional method. Later we shall discuss the shortcut method.

  
  

Conventional Method

Let "X" ml of water to be added to the solution 

Water (ml) + Milk (ml) = Total Solution (ml)
	Water	Milk	Solution
Original	(100 – 10)% of 500 = 90% of 500 = 450	10% of 500 = 50	500
Add	X		X
Total	(450 + x)	50	(500 + x)

Now,

50/(500 + X) = 8/100

(500 + X) = 625

so, X = 125 ml

Now lets have a look at the shortcut method

Shortcut Methhod

This method is applicable only when the impurity level of one of the components of the mixture id reduced in the mixture is reduced in the resultant solution. This method makes use of only 3 values, as given in the question viz

1. Quantity of Original Total Solution = 500 ml
2. Original Level of 'Impurity' = 10%
3. The desired level of 'Impurity' = 8%

Now, the application proceeds as follows:

Original level of Impurity (10%)

                                                       ⇙                                                ⇘

                    Desired Level of Impurity(8%)                    Differenece (10% - 8%) = 2%

Quantity of Pure water to be added

(Difference in level of impurity / Required level of impurity)       

X (Quantity of Original Solution)

⇒ (2% / 8%) * 500 = 125ml

So, 125ml water should be added to get 8% milk.....

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