How to Solve Mixture and Alligation Questions? Know important Tips & Tricks

What is Mixture & Alligation?

As the name implies, a mixture is the combination of two or more items, and alligation allows us to determine the ratio in which the ingredients/materials have been combined and at what price they are sold to generate profit or loss.

Alligation is used to identify the mean value of a mixture when the ratio and amount of the ingredients blended are varied, as well as to find the proportion in which the elements are mixed, in order to solve mixture and alligation questions.

Importance of Mixture & Alligation in Bank Exam

• This chapter is very closely related to the ratio and proportion concept.
• So first clear basic concepts of the ratio-proportion chapter.
• You can expect 2-4 questions from this chapter.
• Also in the main exams, you can expect DI related to this chapter.
• With proper conceptual clarity and practice, you can easily solve these questions.

You can practice important questions from the mixture and allegation chapter in the BYJU'S Exam Prep Bank PO Test Series.

Important Rules of Alligation 

(i) To find the mean or average value of mixture: When the prices of two or more ingredients which may be mixed together and the proportion in which they mixed are given (this is alligation Method); and

(ii) To find the proportion in which the ingredients at given prices must be mixed to produce a mixture at a given price. This is alligation Alternate.

Note:

(1) The word alligation literally means linking. The rule takes its name from the lines or links used in working out questions on a mixture.

(2)Alligation method is applied to a percentage value, ratio, rate, prices, speed, etc and it is not applicable for absolute values. It means whenever percent, per hour, per kg, per km, etc, are being compared, we can use alligation.

Formula of Alligation

if the gradients are mixed in a ratio, then

We represent it as under:

Then, (cheaper quantity) : (dearer quantity) = (d – m ) : (m – c)

Solved problems:

Ex1:  In what proportion must rice at Rs3.10 per kg be mixed with rice at Rs3.60 per kg, so that the mixture be worth Rs3.25 a kg?

Solution:

By the alligation rule :

they must be mixed in the ratio of 7 :3.

You can check other quantitative Aptitude study materials here:

Milk and Water Problems in Alligation

Ex2: A mixture of a certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk is worth Rs1.08 per liter, how much milk is there in the mixture?

Solution:

.

By the alligation Rule, milk and water are in the ratio of 5: 1.

quantity of milk in the mixture = 5 ×16 = 80 litres.

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Ex3: 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% of the solution?

Solution:

The existing solution has 40% sugar, and sugar is to be mixed; so the other solution has 100% sugar. So, by alligation method;

the two mixtures should be added in the ratio of 5: 1

Therefore, required sugar =(300/5)*1 = 60

Direct formula :

Quantity of sugar added =

In this case,

Ans = 300(50-40)/100-50 

=  600 gms

Question: The container contains 75 liters of pure honey. 2/5th of the pure honey is replaced by milk in the container. Again two-fifth of the mixture is extracted and an equal amount of milk is added. What is the ratio of honey to milk in the new mixture?

Answer: Total quantity of pure honey in container = 75 liters 
Quantity of pure honey in container = 75 liters 
2/5th of the pure honey is replaced by milk in the container. Again two-fifth of the mixture is extracted and an equal amount of milk is added. 
⇒ The operation took place 2 times and the amount replaced each time is 2/5 
∴Amount of honey left after 2 operations = 75( 
⇒ Amount of honey left after 2 operations = 75( 
⇒ Amount of honey left after 2 operations = 75 × 9/25 
⇒ Amount of honey left after 2 operations = 27 liters 
Now, required ratio =  
Hence, the ratio of honey to milk in the new mixture is 9: 16

To score well in the Quantitative Aptitude section, attempt quizzes from the given link below -

Quantitative Aptitude Quizzes 

The chapter can be useful for the following exams:

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