Mixture & Alligation
A mixture is the physical combination of two or more different substances or ingredients. These ingredients can be liquids like milk and water, or solids like two different qualities of rice. Alligation is a mathematical rule used to solve problems related to these mixtures. It is a short-cut method to find the ratio in which two items are mixed to get a final price or quality. We often use this rule when we know the individual values and the target average value.
Concepts (3)
This applies when a fixed amount of liquid is removed from a container and replaced with another liquid (like water) multiple times. It is common in milk-water problems.
This applies when a fixed amount of liquid is removed from a container and replaced with another liquid (like water) multiple times. It is common in milk-water problems. If 'x' amount is replaced 'n' times from a total volume 'V', we use a specific formula to find the remaining original liquid. Example: Removing 5 litres from 50 litres of pure milk and replacing it with water twice.
This rule helps find the ratio of ingredients. We place the Cheaper value on the top left and the Dearer value on the top right. The Mean value goes in the center. We subtract diagonally. (Dearer - Mean) gives the quantity of the Cheaper item.
This rule helps find the ratio of ingredients. We place the Cheaper value on the top left and the Dearer value on the top right. The Mean value goes in the center. We subtract diagonally. (Dearer - Mean) gives the quantity of the Cheaper item. (Mean - Cheaper) gives the quantity of the Dearer item. Example: Mix rice at 40/kg and 60/kg to get a mix at 45/kg. The ratio is (60-45):(45-40), which is 15:5 or 3:1.
This is used when the ratio of ingredients is already known. It helps find the final price of the mixture. You multiply each quantity by its price, add them together, and divide by the total quantity.
This is used when the ratio of ingredients is already known. It helps find the final price of the mixture. You multiply each quantity by its price, add them together, and divide by the total quantity. For example, if you mix 2 kg of sugar at 10/kg with 3 kg of sugar at 20/kg, the average price is [(2x10) + (3x20)] / (2+3) = 80/5 = 16/kg.
Ready to practice? Start an interactive lesson.
Start Lesson: Repeated Dilution