Allegation and Mixtures Arithmetic problems simple to complex problems abd concept in detail explanation in video format
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Welcome to Allegation and Mixtures! This is a powerful mathematical technique used to solve problems involving the mixing of different ingredients or substances at various prices or concentrations. The goal is to determine the correct ratio for mixing to achieve a desired average price or concentration. Let's explore this concept step by step.
The basic allegation rule is fundamental to solving mixture problems. When two ingredients at different prices are mixed, the ratio of mixing is inversely proportional to their differences from the mean price. If ingredient A costs 20 dollars and ingredient B costs 30 dollars, and we want a mixture at 25 dollars, then d1 equals 5 and d2 equals 5, giving us a ratio of 1 to 1.
Let's solve a simple problem. We want to mix rice at 40 dollars per kilogram with rice at 60 dollars per kilogram to get a mixture at 50 dollars per kilogram. First, we calculate d1 equals 50 minus 40 equals 10. Then d2 equals 60 minus 50 equals 10. Therefore, the ratio is d2 to d1, which is 10 to 10, or simply 1 to 1. This means we need equal parts of both types of rice.
Now let's solve a more complex problem. A shopkeeper has tea at 80 dollars per kilogram and 120 dollars per kilogram. He wants to make a blend at 100 dollars per kilogram. If he uses 20 kilograms of the cheaper tea, how much expensive tea should he use? First, we calculate the differences: d1 equals 20 and d2 equals 20, giving us a ratio of 1 to 1. Since he uses 20 kilograms of cheaper tea, he needs 20 kilograms of expensive tea, making a total of 40 kilograms of blend.
Allegation and mixtures have wide applications in business for profit calculations, chemistry for solution concentrations, cooking for recipe adjustments, and finance for investment portfolios. Remember the key steps: find differences from the mean price, use the inverse ratio rule, apply to given quantities, and always verify your answer. The allegation rule states that the ratio of quantities is equal to d2 over d1, where d1 and d2 are the absolute differences from the mean price. Master this technique and you'll solve mixture problems with confidence!