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What are Allegations?
The study of the mixture is common. In every subject questions related to mixtures is very common and frequently asked.
Allegations are an old used technique used to solve mathematical and algebraic equations related to the mixing of two mixtures.
A mixture is defined as a result of two or more solutions mixed in a definite proportion.
In simple words, an allegation is defined as a rule that provides us help to quickly calculate the amount of a mixture in different proportions, keeping in mind that the mixture is a result of only two elements mixed in a specific measured proportion/amount.
Mean Price is defined as the average cost price of a single quantity of a solution which is a result formed of mixing two or more elements.
Rules of allegations state that if two items/elements at a mentioned price are mixed to produce a result/solution at that given price then, the basic formula used to find the ratio in which the ingredients are mixed is
Quantity of cheaper / Quantity of dearer = (Cost price of dearer – Mean price) / (Mean price – Cost price of cheaper)
It is also called the rule of the allegation and a simple representation of this is:
Quantity of cheaper ingredient/ Quantity of costlier ingredient = (d-m)/ (m-c)
There are various types of questions and problems related to Allegations, some of them are-
1: The problem will state the number of ingredients and the proportion in which they are mixed and then the question will be asked to find the average amount of the mixed result.
2: The problem will state a needed amount/quantity of the mixture as well as the amounts of the mixed elements. A question will be asked to know in what proportion are the two elements mixed to get the required amount.
3: To know the proportion of the final result when it undergoes concentration or dilution.
4: Determine the proportion in which the given two elements must be mixed to determine for how much profit or price will the solution be sold.
To find the average of the weight of the result, or if the proportions of both the mixed elements are given along with the cost at which one unit of that resulted mixture will be sold then
The cost price of the cheaper element is denoted by ‘c’.
The cost price of an expensive element is denoted by ‘d’.
Mean price is denoted by ‘m’.
The amount of ingredient which is cheaper/ the amount of ingredient which is expensive = d – m / m – c
Examples-
- In what ratio must a bartender mix two elements of a juice worth Rs.50 per kg and Rs.100 per kg so that the average cost of the resulted mixture is Rs.70 per kg?
Solution-
Price at which one kg of the mixed result will be sold = Rs.70.
Price of the cheaper element = Rs.50.
Price of the expensive element = Rs.100.
Cheaper quantity/Expensive quantity = (100 – 70)/ (70 – 50) = 30/20 = 3/2 = 3:2.
Therefore, the ratio in which the bartender must mix the two elements is 3:2.
- In what ratio must a bartender mix two elements of a juice worth Rs.60 per kg and Rs.150 per kg so that the average cost of the resulted mixture is Rs.100 per kg?
Solution-
Price at which one kg of the mixed result will be sold = Rs.100.
Price of the cheaper element = Rs.60.
Price of the expensive element = Rs.150.
Cheaper quantity/Expensive quantity = (150 – 100)/ (100 – 60) = 50/40 = 5/4 = 5:4.
Therefore, the ratio in which the bartender must mix the two elements is 3:2.
- In what ratio must a bartender mix two elements of a juice worth Rs.70 per kg and Rs.100 per kg so that the average cost of the resulted mixture is Rs.80 per kg?
Solution-
Price at which one kg of the mixed result will be sold = Rs.80.
Price of the cheaper element = Rs.70.
Price of the expensive element = Rs.90.
Cheaper quantity/Expensive quantity = (100 – 80)/ (80 – 70) = 20/10 = 2/1 = 2:1.
Therefore, the ratio in which the bartender must mix the two elements is 2:1.
Conclusion-
The allegation is a fun topic to learn and perform sums on. It helps one challenge his/her mental thinking capacity and common knowledge skills. Mixing and forming new substances with a mixture of business is what makes this topic important for us and helpful.
Conclusion
Thus, both simple and compound interest comes with their set of advantages and disadvantages from a financial perspective. Hence, it is essential for the person to calculate it well before proceeding ahead.
