Mixture & Alligation Problems Will Not Be Difficult For You Anymore

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Dear Reader, many youngsters find mixtures and allegation very difficult. But it is very easy if you understand the diagram based rule which we will see below. This tutorial will help you to prepare important 2 types of problems you can expect in bank exams.

At the end of the topic, don’t forget to take the online test. This will help you to test yourself.

Now, here is your tutorial.

Type I: Finding Ratio Of Mixture Of Two Items If Prices Are Given

In this type, you will be given two varieties of same item or two different items. Both will have different prices. Then, they will be mixed together in some ratio. You will be given the final price of the mixture. You have to find the ratio of mixture.

This type is very easy if you know the diagram based rule. You will understand this rule after reading the below example.

Example Question 1: In what ratio must rice at Rs.12 per kg be mixed with rice at Rs.15 per kg so that the mixture be worth Rs.14 per kg?

Solution:
To solve this problem, first look the below diagram carefully. You will find explanation after the diagram.


In the above diagram, first box (Box A) represents cost price of cheaper item. In our example question, the CP of cheaper variety of rice is Rs.12 per Kg.

Second box (Box B) represents cost price of costlier item. In our example question, CP of costlier variety of rice is Rs.15 per Kg.

Middle box (Box C) represents cost price of the mixture. In our question, CP of the mixture is Rs.14 per Kg.

If you substitute the above three values, the diagram becomes :


Now, you have to find the ratio of the mixture. You can find the ratio using the below formula:
Ratio of cheaper item to costlier item = (CP of Costlier item – CP of Mixture) / (CP of Mixture – CP of Cheaper Item)
= (15 – 14) / (14 – 12)
= 1:2

So, what is your inference?
You have to mix cheaper variety of rice and costlier variety of rice in the ratio 1:2 so that the price of the mixture will be Rs.12 per Kg.

Type 2: Finding Quantity From Ratio Of Mixture

This type is an extension to type 1. In this type, first you have to find the ratio like type 1. Then you have to find the quantity of any one item (quantity of the other item will be given).

Below example will help you to understand this type well. Read on…

Example Question 2: How much water should be added to 50 litres of lemon extract if 2 litres of lemon extract is bought for Rs.30 and the price of the mixture should be Rs.5 per litre?

Solution:
From the question, you know that the cost price of 2 litres of lemon extract is Rs.30.
Since the diagram and formula are based on price per litre, you have to find the price of lemon extract per litre.
CP of 2 litres of lemon extract = 30
Therefore, CP of 1 litre of lemon extract = 30/2 = Rs.15

The other item in the mixture is water. Since price of water is not given, you can assume water is free of cost (rarely it is the case nowadays :)).
CP of 1 litre of water = Rs.0

From the question, you know the CP of the mixture = Rs.5
If you substitute the above three values, you will get the below diagram.


You already know the below formula:
Ratio of cheaper item to costlier item = (CP of Costlier item – CP of Mixture) / (CP of Mixture – CP of Cheaper Item)

In our case cheaper item is water and costlier item is lemon extract
Therefore, the above formula becomes
Ratio of water to lemon extract = (CP of Lemon Extract – CP of Mixture) / (CP of Mixture – CP of Water)
= 15 – 5 / 5 – 0 = 2:1

Till now, this is same as type 1. Now comes the interesting part. In question, you are asked to find the amount of water to be added to 50 litres of lemon extract.

You have already found that the ratio of water to lemon extract = be 2:1
In other words, for every 1 litre of lemon extract, you have to add 2 litres of water.
So for 50 litres of lemon extract, you have to add 2 x 50 = 100 litres of water

Above is a simple calculation right? If you find it difficult, you could use direct proportion table method as shown below

Quantity Of Lemon Extract Quantity Of Water
1 2
50 X

1/50 = 2/X
Or X = quantity of water to be added to 50 litres of lemon extract = 2 x 50 = 100 litres

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