Thursday, 18 May 2017

Mixtures and Alligation I - Introduction and formulas to solve Mixtures and Alligation Questions

In this post, we will discuss mixtures and alligation questions and solve them using formulas in IBPS PO and SSC CGl Exams
Mixtures and Alligation

Every SBI PO, IBPS PO and SSC CGL Exams contain allegation and mixtures questions. Mixtures and alligation questions from this section of quantitative aptitude are word problems on ratio and proportion, percentages or average weighted averages. Most of you try to ignore mixtures and alligations questions because of the too much content in it or by too much time taken by the mixtures and alligation questions in IBPS PO and SSC CGL Exams.

In this post, we will focus on formulas that will help you solve Mixtures and alligation questions easily and also use the pictorial method of representation which will make it easy for you to understand the question and solve them without any trouble.

What is a Mixture?

A mixture contains two or more ingredients of certain of certain quantity mixed together to get the desired quantity. The quantity can be expressed as ratios or percentage.

When two varieties of rice are mixed to form a new variety of rice then it is called as a mixture.

What is an Alligation?

If two ingredients A and B of price x and y 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 the alligation

An alligation is the rule that enables us to find the ratio in which two or more ingredients at a given price or value must be mixed to produce a mixture at a given price (Value or Strength).

Formulas for Mixtures and alligation questions for IBPS PO And SSC CGL Exams. 
Mixtures and Alligation
Mixtures and Alligation
Mixtures and Alligation

Pictorial representation of Mixtures and Alligation
Mixtures and Alligation
Model 1: Mixtures and Alligation

Example 1Mixtures and Alligation Questions for IBPS PO and SSC CGL Exams

Question: How much of salt at 42 paise/kg must be mixed with 25kg of salt at 24 paise/kg, so that a profit of 25% is obtained by selling the mixture at 40 paise /kg?

Th question is based on a combination of two different varieties of salt to obtain a mixture at the given price.
In this question, we are suppose to find the quantity of salt which costs 42 paise that is mixed.
So, we need to find the ratios of the quantity to find the quantity of salt that is mixed.

Step 1:
First, we need to find the price of the mixed salt, that is
Profit = 25% 
Selling Price = 40 paise/kg
Cost of the Mixture = 32 paise

Step 2:
Use the pictorial representation method to find the ratios.
Mixtures and Alligation
Step 3:
The ratio = 4 : 5 
Quantity(dearer) : Quantity (Cheaper) = 4 : 5
Quantity(dearer) : 25 = 4 : 5 
Quantity(dearer) x 5 = 4 x 25 
Quantity(dearer) = 100/5 
Quantity(dearer) = 20kg

Therefore, The 20kg of dearer quantity is supposed to be mixed with 25kg of cheaper quantity to make a new mixture of salt.
Mixtures and Alligation 
Example 2: Mixtures and Alligation Questions for IBPS PO and SSC CGL Exams

Question: A merchant has 840kg of rice, part of which he sells at 9% profit and the rest at 16% profit. He must gain 12% profit on the whole. What is the quantity sold at 16% profit?


Step 1:
By applying the alligation rule on the profit percentages
Mixtures and Alligation
Step 2:
Quantity (sold at 9% profit): Quantity (sold at 16% profit) = 4 : 3
840: Quantity (sold at 16% profit) = 4 : 3 
Quantity (sold at 16% profit) = (3 / 7) x 840 (by the basis of ratio and proportion, we need to take the whole part i.e. 4 + 3 = 7)
Quantity (sold at 16% profit) = 360Kg.
Therefore, 360Kg is the quantity that is sold at 16% profit.
Do write in the comment section how this blog helped you to solve mixtures and alligation questions using mixture and alligation formula.
Stay tuned for more mixtures and alligation questions. 
Mixtures and Alligation
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