Rule of Alligation

Introduction 

Mixtures are those compounds that are made by mixing two or more two substances, which can be liquid or solid or even semi-solid. In order to make a suitable mixture, the proportion in which the substances are being mixed needs to be calculated and identified. Ratio and proportion and alligation are the two major concepts that help one to make the required mixture. However, on the other hand, if one wants to know in which quantity the substances are being used in a particular mixture, then it can also be done by calculating the alligation formula.       

Discussion 

Concept of alligation

Alligation is associated with mixtures, where mixtures are those substances that are made through mixing two or more substances in particular ratios. Each substance used in the mixture has different strengths and different proportions. Often it becomes essential for determining in which proportion they are added or what is the strength of each element. Alligation formulas provide the scope to calculate the required aspects. Pharmacists need to know in what proportions the medicines needed to be mixed to cure a certain disease. In the field of chemistry, this concept has a significant contribution, however, several other problems associated with wages or partnerships can be easily solved with the help of an alligation grid. Calculating answers for time and work problems are often quickly determined through the same. Hence, the alligation grid and the formula are essential in several aspects. The alligation rule helps us in dealing with mixtures so that we can easily make substances by mixing several ingredients.  Among the alligation types, which are medial and alternate, alternate is much more complex and difficult to solve. In school textbooks, there are several topics like percentage, profit and loss or simple interests which can be easily and quickly solved through an alligation grid.        

What is the rule of alligation? 

Looking into the question, what is the rule of alligation can be answered in a few basic steps, which first involves a grid. The grid is basically made of 5 blocks with four at the four corners, and one at the center. Outward directing arrows are present, which start from the center block and point towards the rest four blocks. In the topmost two blocks, cost prices of the cheaper and dearer materials are present, whereas in the bottom-most blocks the difference values are present. Like on the right-hand side, the difference between the mean price and CP of a single unit of cheaper substance is calculated, and on the left-hand side, the difference between the cost price of the dearer elements and the mean price is noted. At the center value of the mean, price is calculated and noted.  A few factors associated with the grid is as follows: 

• While determining the difference between extreme values and corresponding average prices, always the smaller value is deducted from the larger one. As a result the final value thus obtained is always positive.
• Differences are always placed on the same side. 
• Through the grid, the final ratio is calculated which tells about the level of price under which the product is visible.
• Any problem which has two extreme values and their averages then it can be done with the help of the grid. 

In the formula, percentages are represented in percentages, solid and semi-solid substances are calculated in grams, whereas liquids are taken in milliliters.        

Procedure to solve problems through alligation

There is a basic formula, where on the left-hand side the amount of cheaper element taken is divided by the dearer one and on the right-hand side, the two differences are divided. CP  of a single unit of the dearer element is subtracted from the mean price is put in the numerator, while the mean price is subtracted from the CP of a single unit of the cheaper unit is noted in the denominator. Since numerators, as well as denominators, are positive so the whole ratio is positive in total. Here CP represents the cost price of each element.  

Looking onto the tricks or procedures to solve problems with the help of an alligation grid is as follows:

• The left box at the top is occupied by a higher strength value.
• The bottom left box is filled with comparatively lower strength.
• The center block is filled with the value of desired strength.  
• The difference between higher strength and the desired value is placed at the right-hand side of the bottom block. 
• The difference between lower strength and mean value is noted in the topmost right block. 
• Values situated on the right-hand side were added which represents the total parts of the whole system.  
• Value of parts needed upon total parts is calculated which is further needed. 
• Hence by adding, the result is found.   

Conclusion 

Alligation is an essential concept in the topic of mixtures, as it helps one in determining in what proportion substances are being used to form a particular substance. Each and every ingredient which is being used in the mixture varies in strength, alligation formulas help in determining the strength of any ingredient. Any required value whether it is the strength or proportion of a substance in the mixture can be either determined through formula or even with the help of a grid. The significance of alligation can be found in solving problems associated with partnerships, time and work and issues with wages.