Alligation finds the ratio in which two ingredients at different prices (or concentrations) must be mixed to get a mixture at a given mean price.
1Rule of alligation
Cheaper quantity : dearer quantity = (dearer price − mean price) : (mean price − cheaper price)
2Repeated replacement
A container holds x units of liquid; y units are removed and replaced with water n times. Liquid left = x(1 − y/x)ⁿ