Alligations Questions with Solutions

Alligation is a quick method for finding the ratio in which two ingredients at different prices or concentrations must be mixed to get a mixture at a given mean price or concentration. The rule of alligation is: (cheaper quantity) : (dearer quantity) = (dearer price - mean price) : (mean price - cheaper price). Exam questions involve mixing two varieties of rice, tea or other goods, milk and water mixtures, solutions of different concentrations, and replacement problems, where part of a mixture is removed and replaced with water again and again. For repeated replacement, the quantity of the original liquid left is x(1 - y/x)^n, where x is the total quantity, y is the amount removed each time and n is the number of operations. Alligation also works for averages, speeds and profit percentages, which makes it a powerful shortcut across many topics. Practise the alligation and mixture questions below, each with a step-by-step solution.