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RRB NTPC 2019 has around 35,000 vacancies and government job aspirants across the country have applied for this exam. These vacancies are for both Graduates and Non-Graduates across Zonal Railways and Production Units of the Indian Railways. Because of some reasons the RRB NTPC exam dates have been continuously postponed. But the good news is that the Phase I exam will take place on December 15 onwards. Are you ready for this exam? Check your preparation level by taking a mock test of RRB NTPC. The best part is that the 1st mock test is free of cost. In this exam, 1-2 questions are generally asked from Mixture & Alligation. And therefore, in this article we will be covering its concept and discuss some examples along with tips to solve the questions quickly and with accuracy.

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## Understanding Mixture & Alligation

Mixture, basically refers to mixing of two or more components together and can be a simple mixture (i.e. mixing of two or more ingredients together) or complex mixture (i.e. mixing of two or more simple mixture together). On the other hand, Alligation helps to find the ratio in which two or more ingredients at a given price should be mixed to produce a mixture of the desired price.

The Alligation is applied to a percentage value, rate, ratio, price, speed or anything else and so it is not applicable for absolute value. Hence, alligation can be used whenever we are comparing percent, per hour, per kg, per km, etc. The rules of alligation are simple:

(Quantity of Cheaper)/(Quantity of Dearer) = (Cost Price of Dearer – Mean Price)/(Mean Price – Cost Price of Cheaper)

or can be represented as:

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

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## Example 1:

In what proportion should rice at Rs 13.40 per kg be mixed with rice at Rs 13.65 per kg, so that the mixture be worth of Rs 13.20 per kg?

Solution: The correct answer is 9:4. Let us solve this by taking help from the diagram that we had drawn earlier.

(Quantity of Cheaper Rice)/(Quantity of Dearer Rice) = 45/20 = 9/4

## Example 2:

500 grams of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% of the solution?

Solution: 100 grams of sugar should be added. We can quickly solve this question by first finding out the ratio in which the proportion should be mixed followed by calculating the sugar weights that need to be added. Please note that the existing solution has 40% sugar, and sugar is to be mixed. SO the other solution will have 100% sugar.

(Sugar Solution)/(Sugar) = 50/10 = 5/1

Hence, the amount of sugar that needs to be added shall be: (500 / 5) * 1 = 100 grams

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## Example 3:

In a 40 litres mixture acetic acid and sodium acetate are in the ratio 3:1, find the amount of sodium acetate solution to be added to make the ratio 2:3?

Solution: The correct answer is 35 litres. The proportion of sodium acetate is 25% (since original mixture is 3:1, i.e. acetic acid is 75% and sodium acetate is 25%), and we need to find the amount of sodium acetate that needs to be added to make the ratio 2:3 (i.e. acetic should be 40% and sodium acetate should be 60%). Hence, while drawing the diagram, we should consider the sodium acetate quantity. The diagram should look like the following:

(Sodium Acetate Solution) / (Sodium Acetate) = 40/35 = 8/7

Hence, the amount of sugar that needs to be added shall be: (40 / 8) * 7 = 35 litres

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## Example 4:

A container contains 75 litres of pure milk. Two-fifth of the milk is replaced by honey in the container. Further, two-fifth of the mixture is extracted and an equal amount of milk is added. What is the ratio of milk to honey in the new mixture?

Solution: The ratio of milk to honey in the new mixture is 9:16. This is a removal type of question and may appear in the exam. The best way to approach this question is by following the below steps:

Step 1: Compute the amount of milk that is withdrawn from the original solution. Since this operation was followed twice, we will have to use square, while computing the withdrawal.

= 75 x 25/9

= 27 litres (This is amount of milk removed from the container)

Step 2: Calculate the required ratio

= 27 / (75 -27)

= 27 / 48

= 9 / 16 or 9:16 (The new ratio of milk to honey)

## General tips:

1. Do not rush to answer the question with reading and understanding the requirements of the question.
2. Try to draw the diagram whenever you encounter questions on alligation as this will not only save a lot of time but also ensure that you do not get wrong anywhere.
3. In case you are comfortable solving these types of questions in traditional ways by using formulas then you may follow that, however, that will take some time.
4. The trick to solving these types of questions quickly is by practising several questions in a controlled environment. For this, we would suggest you take mock tests that will expose you to a variety of such types of questions. Further, these test series will also help you to understand the areas where you are strong and where you need to pay more attention.
5. Practice a lot of questions of Mathematics section (specially Mixture and Alligation) for free and compare your score with that of other competitors.

We hope this article will be helpful in your preparation and wish you all the best for your exam. Don’t forget to keep taking mock tests to have a continuous assessment of your preparation. Keep working on your mistakes and your score will definitely improve.

Happy learning!