MIXTURE AND ALLIGATION FOR COMPETITIVE EXAMS
Introduction
The words Mixture and Alligation are mostly used in the Quantitative aptitude section of the various Government exams. But what do they exactly mean? What are the formulas used to solve these concepts? In this article, we have discussed the concept of mixture and allegation in detail with tips and tricks, important formulas to solve questions based on the topic.
(Read More: How to solve the BODMAS questions? Let's explore!)
What is Mixture and Alligation?
Mixture refers to the mixing of two or more in a fixed ratio or proportion. Usually, mixtures are prepared by mixing solids, liquids or gases with other solids, liquids or gases.
Alligation is a concept or rule that helps us in solving the problems related to mixture. It helps us in finding out the ratio in which two substances, having a specified cost, must be fixed to obtain a final mixture having ingredients in a certain ratio.
The number of questions asked from the quantitative aptitude section varies between 1-3 and a little complex to solve. Aspirants preparing for the toughest exams in India like UPSC, SSC CGL, JEE, must practice thoroughly to answer questions from this topic.
Mixture & Alligation - Quantitative Aptitude for Government Exams
While solving mixture and alligation questions, one must remember that alligation as a concept is used to find the mean value of a mixture when the ratio and amount of the substances are mixed. Candidates applying for the government exams can refer to the sample test papers online for enhanced preparation.
Important Formulas for Mixture and Alligation
To solve any numerical questions, it is very crucial to know a set of formulas for every topic which helps in solving the questions easier. Below are a few formulas which will help you in solving Mixture and Alligation questions:
(Know More: What does quadrilateral mean? Lets know their properties!)
The basic formula used to solve Mixture and alligation concept are:
It is also called as rule of Alligation and can be represented as:
Tips and Tricks To Solve Questions
Time management plays a key role during competitive exams. Students can’t afford to lose a lot of time while solving any tricky questions. Thus, we have provided a few simple tips and tricks to solve the mixture and alligation problems easily. Get familiar with the concepts to avoid confusion and make notes of all the important formulas.
Below are the rules of aligation which are used to solve questions related to partnerships, time and work and wages
Tip 1: Componendo rule: If a/b = c/d then a+b / b = c+d / d
Tip 2: Dividendo rule: If a/b = c/d then a-b / b = c-d / d
Tip 3: Componendo & Dividendo rule: If a/b = c/d then a+b / a-b = c+d / c-d
Tip 4: Invertendo rule: If a/b = c/d then b/a = d/c
Tip 5: Alternendo rule: If a/b = c/d then a/c = b/
Questions based on Mixture and Alligation
Q 1. A grocery store owner wishes to sell a mixture of two varieties of pulses worth Rs.16 per kg. In what ratio must he mix the pulses to reach this selling price, when the cost of one variety of pulses is Rs.14 per kg and the other is Rs.24 per kg?
1. 2:5
2. 4:3
3. 2:1
4. 4:1
5. 7:6
Answer: (4) 4:1
Solution:
Using the rule of alligation,
Quantity of Dearer/ Quantity of cheaper= 24-16/ 16-14
⇒ 8:2 = 4:1
Q 2. Cost of two types of pulses is Rs.15 and Rs, 20 per kg, respectively. If both the pulses are mixed together in the ratio 2:3, then what should be the price of a mixed variety of pulses per kg?
1. Rs. 22 per kg
2. Rs. 30 per kg
3. Rs. 10 per kg
4. Rs. 18 per kg
5. Rs. 24 per kg
Answer: (4) Rs. 18 per kg
Solution:
Let the cost of mixed variety of pulse be Rs. x
As per the alligation rule,
2:3 = (20-x) : (x-15)
⇒ 2x+3x = 60+30
⇒ 5x = 90
⇒ x = 18
Q 3. A dealer has 1000 kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit he earns is 14%. What is the quantity which is sold at 18% profit?
1. 250 kg
2. 600 kg
3. 620 kg
4. 400 kg
5. 450 kg
Answer: (2) 600 kg
Solution:
As per the rule of alligation,
Quantity of Dearer: Quantity of Cheaper = (18-14): (14-8) = 4:6 = 2:3
Quantity of sugar sold at 18% profit = 3/5 × 1000 = 600kg
Q 4. How much coffee of variety A, costing Rs. 5 a kg should be added to 20 kg of Type B coffee at Rs. 12 a kg so that the cost of the two coffee variety mixture be worth Rs. 7 a kg?
1. 25 kg
2. 34 kg
3. 55 kg
4. 52 kg
5. 50 kg
Answer: (5) 50 kg
Solution:
As per the rule of alligation,
Quantity of Dearer: Quantity of Cheaper = (12-7) : (7-5) = 5:2
Quantity of Variety A coffee that needs to be mixed ⇒ 5:2 = x:20
⇒ x =50 kg
