Types of Partnership and Kinds of Partners

Partnerships are described in a few standard ways. A Business Mathematics problem will usually reveal which situation applies through the numbers it gives rather than by naming it, but the vocabulary is worth knowing.

By how capital and time are contributed — this is the distinction that actually drives the arithmetic:

• Simple partnership — every partner's capital stays invested for the same period of time (typically the whole year). Because the time is common to everyone, it cancels out, and profit is shared purely in the ratio of the capitals.
• Compound partnership — partners' capitals stay invested for different periods of time. Here time cannot be ignored, and profit is shared in the ratio of each partner's capital multiplied by the time for which it was invested.

By the role a partner plays:

• An active (or working) partner takes part in the day-to-day running of the business. Because of the extra effort, a working partner is often allowed a salary or commission out of the profit before the balance is divided.
• A sleeping (or dormant) partner contributes capital but does not take part in running the business, and so shares only in profit, without any salary.

By the scope and duration of the firm — mentioned for completeness, as these rarely change the arithmetic:

• A partnership at will has no fixed period and continues until a partner chooses to end it; a particular partnership is formed for a single venture or a fixed term and ends when that is complete.
• In a general partnership every partner has unlimited liability for the firm's debts; in a limited partnership at least one partner's liability is restricted to the capital they put in. …