Simple Partnership — Sharing in the Ratio of Capitals

In a simple partnership all partners' capitals remain in the business for the same length of time. Since the time is identical for everyone, it plays no part in the division, and the profit is shared directly in the ratio of the capitals.

If two partners invest capitals $C_1$ and $C_2$ for the same period, then $\text{Profit of first partner} : \text{Profit of second partner} = C_1 : C_2.$ For any number of partners with capitals $C_1, C_2, C_3, \dots$ invested for equal times, the profit is divided in the ratio $C_1 : C_2 : C_3 : \dots$. To turn a ratio into an actual amount of money, convert each partner's ratio term into a fraction of the total: $\text{Partner's share} = \frac{\text{that partner's ratio term}}{\text{sum of all ratio terms}} \times \text{Total profit}.$

For example, if the capitals are in the ratio $2:3$ and the total profit is $15000$ rupees, the total number of ratio parts is $2+3=5$, so one part is worth $\frac{15000}{5}=3000$ rupees; the two partners then receive $2\times 3000 = 6000$ and $3\times 3000 = 9000$ rupees respectively. …