Partnership

When two or more than two persons run a business jointly, they are called partners in the business and the deal between them is known as partnership.

Partnership is of two types

1. Simple Partnership
2. Compound Partnership

1. Simple Partnership: When investments of all the partners are for the same period of time, the profit or loss is distributed among the partners in the ratio of their original investments.
Suppose A and B invest Rs. p and Rs. q respectively for a year in a business, then at the end of the year. Share of A’s profit (loss) : Share of B’s profit (loss) = p : q.

2. Compound Partnership: When investments of all the partners are for different period of time, then equivalent capitals are calculated for a unit of time and the profit or loss is divided in the ratio of the product of time and investment.
Suppose A and B invest Rs. p and Rs. q for x months and y months respectively, then Share of A’s profit (loss):
Share of B’s profit (loss) = px : qy. Partners are of two types
(i) Working Partner, and
(ii) Sleeping Partner

(i) Working Partner: A partner who manages the business is called a working partner.
(ii) Sleeping Partner: A partner who only invests the money is called a sleeping partner.

Example 1: A and B started a business with capitals of Rs. 25000 and Rs. 40000 respectively. Find the share of A and B out of an annual profit of Rs. 6500.
Solution. Ratio of shares of A and B = Ratio of their investments = 25000 : 40000 = 5 : 8

Example 2: A, B and C start a business each investing Rs. 16000. After 3 months A withdrew Rs. 2000, B withdrew Rs. 4000 and C invests Rs. 8000 more. At the end of year a total profit of Rs. 41580 made. Find the share of A, B and C

Solution. Ratio of capitals of A, B and C
= (16000 × 3 + 14000 × 9) : (16000 × 3 + 12000 × 9) : (16000 × 3 + 24000 × 9)
= 174000 : 156000 : 264000 = 29 : 26 : 44

Example 3: A, B and C enter into a partnership with a total of Rs. 8200. A’s capital is Rs. 1000 more than B’s and Rs. 2000 less than Cs. What is B’s share of the year’s profit of Rs. 2,460.
Solution. Given, A = B + 1000 = C – 2000
                           C = B + 3000
A + B + C = (B + 1000) + (B) + (B + 3000)
8200 = 3B + 4000 Þ 3B = 8200 – 4000  B = Rs. 1400