🤝 Profit-Sharing Basics

When every partner keeps their money in for the same length of time, time plays no role and the profit simply splits in the ratio of the amounts invested:

$\text{profit}_A : \text{profit}_B = \text{capital}_A : \text{capital}_B$

• Make the ratio: write the capitals side by side and cancel common zeros, e.g. $4000 : 6000 = 2 : 3$.

• Count the parts: add them up — $2 + 3 = 5$ equal shares in total.

• Find one part: total profit $\div$ total parts. If the profit is $20000$, one part $= 20000 \div 5 = 4000$.

• Scale up: multiply one part by each person's parts. A gets $2 \times 4000 = 8000$.

Hidden ratios: if the question says $3 \times A = 4 \times B$, swap the numbers — $A : B = 4 : 3$ (the one tied to the smaller number is the bigger investor).