Ratio, average & mixture

Average

Average = Sum / Number

Average speed (equal distances)

2xy / (x + y)

Ratio split

Share of A = Total × a / (a + b)

Alligation

Cheaper : Dearer = (d − m) : (m − c)

m = mean price

Repeated replacement

Left = x(1 − y/x)ⁿ

x = total, y = taken out each time

Partnership

Profit share ∝ Capital × Time