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Mixture and alignment are crucial concepts in a quantitative aptitude test. A mixture is a new product created by combining two or more ingredients in a specific ratio. Alligation, in turn, helps us evaluate and find the ratio in which they have been mixed. Alligation also helps us find the price for the ingredients used in the mixture to gauge the profit or loss. Below are a few techniques for solving mixture and alligation problems that help you grasp the concept better.
What is a Mixture?
A mixture is a new product created by combining two or more ingredients in a specific ratio.
Let’s begin with the many forms of mixes.
· Simple mixtures: A simple mixture is generated when two or more different materials are combined. For example, combining milk and water or rice from two different pricing ranges.
· Compound mixtures are created when two or more separate mixtures are combined to generate a compound mixture. For example, mixing two alloys with varying proportions of two or more metals.
Mean Price
The mean price is the cost price of a unit quantity of the combination.
Mean Price and Rules of Allegation or Mixture
When the price of the individual products being mixed and the proportion in which they are combined are supplied, this rule of the mixture is used to find the mean price of the combination.
When two materials with known pricing are known, the ratio in which they are combined to produce a mixture with a known price is known.
1. The mixture’s value is always higher than the lowest and lower than the maximum value of mixed things.
2. For rate, ratio, % value, speed, price, and other numerical values, the rule of mixture or allegation is used, but not for absolute values. This method can be used to compare values per hour, per km, per kg, etc.
3 Steps to Solve Mixture Problems
Let’s look at the steps and formula for solving mixture problems!
Step 1: Set Up the Problem
Three amounts or quantities are involved in mixture problems. The first two are the amounts being mixed, while the third is the total amount of the combination. Each portion has its own cost or percent strength. As a result, the setup follows this principle to the letter.
Solution Problems:
(percent 1) (quantity 1) + (percent 2) (quantity 2)= (final percent ) (amount total)
Problems with Mixtures:
(amount 1) + (cost 1) (cost 2) (ultimate cost) + (amount 2) (total amount)
It’s critical to techniques for solving mixture and alligation problems. Any one of these six bits of data could be unknown. Your task is to fill in all blanks, find out the unknown, and replace it with the letter “x.”
Step 2: Identify the “x”
To solve any mixing issue, you must first find “x.” Let’s look at a challenging one to see how this works in practice.
You require a 15% acid solution for a particular test, but your supplier only has a 10% and a 30% acid solution on hand. Rather than paying extra for him to generate a 15 percent solution, you decide to make your own 15 percent solution by mixing a 10 percent solution with a 30 percent solution. The 15 percent acid solution will require 10 litres. How many litres of a 10% solution and a 30% solution should you use?
Okay, so this one has a unique trick that may frequently appear in these difficulties. You’ll see that we’ve only been provided one numerical value (10 litres). We have two unknowns in this problem: the litres required for the 10% and 30% percent solutions.
This may be an issue, but there is a simple solution. Consider it this way: We need to go to a total of 10 litres. Let’s call the number of litres we’ll need for our 10% solution “x.” So, how many litres will we need for the 30% solution? In total, there are 10 litres. There are X litres left, thus what’s left of our permitted 10 litres is 10-x.
Using this straightforward approach, we may express both of our unknowns in terms of a single variable. It makes no difference which of the quantities we refer to as x and which we refer to as 10-x as long as we maintain track of which is which.
Step 3: Work the Problem
Let’s look at the identical situation again, but this time it only mentions the most important details.
You decide to make your own 15 percent solution by mixing a 10% solution with a 30% solution. The 15 percent acid solution will require 10 litres. How many litres of a 10% solution and a 30% solution should you use?
So, let’s incorporate it into our solution problem arrangement. Let’s keep the percentages in decimal form throughout.
15 = 10 (unknown amount) +.30 (unknown amount 2) (10)
Formulas and Quick Tricks for Mixtures and Alligations
The following are the techniques for solving mixture and alligation problems;
1. Alligation: Alignment is a rule that allows us to determine the proportions in which two or more ingredients at a particular price must be blended to make a mixture of a specific price.
2. Mean Price: The cost price of a unit quantity of the combination is known as the mean price.
3. Rule of Alligation: When two ingredients are combined, (Quantity of cheaper / Quantity of dearer) = (CP of dearer – Mean Price / Mean price – CP of cheaper).
4. If the number of quantities in two groups is n1 and n2 and their average is x and y, respectively, the combined average is (n1x+n2y) / (n1 + n2)
5. If there are n1 and n2 quantities in each group, and their averages are x and y, the combined average is (n1x+n2y) / (n1 + n2)
6. x equals the average of n quantities. The average becomes y when a quantity is removed. n(x-y) + y is the value of the amount deleted.
7. x equals the average of n quantities. The average becomes y when a quantity is added. The new quantity’s value is n(y-x) + y.
Conclusion
A mixture is formed by combining two or more items, and alligation allows us to determine the ratio in which the ingredients/objects were combined to make the mixture. The most important thing to understand when working with mixture and alligation is that alligation is a method for determining the mean value of a mixture, when the ratio and amount of ingredients incorporated vary, and the proportion in which the elements are mixed.
