When two or more than two persons run a business together, they are called partners and the deal is known ad partnership.
There are two kind of partnership:- 
- Simple Partnership
- Compound Partnership
Simple Partnership :- All the partners invest their capital or investment for same period of time.In this case profit earned is divided into the ratio of capital. Lets Understand with example :-
Example :- A and B started a business by investing Rs. 2000 and 3000 respectively for 1 year. Find the share of both, out of an annual profit of Rs. 2500.
Solution :- Here both have invested for same period of time so partnership is simple hence profit is divided into the ratio of capital
A:B = 2000:3000 =2:3
total ratio = 5
Profit of A = (2/5)*2500 = 1000
Profit of B = (3/5)*2500 = 1500
Compound Partnership :- All partners invest their capital for different period of time. Here profit in divided into the ratio of time value of money.
Time value of money = capital * time
Example :- A and B started a business by investing Rs. 2000 and 3000 respectively in which A invested for 1 year and B for half year. Find the share of both, out of an annual profit of Rs 3500.
Solution :- Here both have invested for different period of time so partnership is compound hence profit is divided into the ratio of time value of money
A:B = 2000*12 : 3000*6 =24000 : 18000 = 4:3
total ratio = 7
Profit of A = (3500/7)*4 = 2000
Profit of A = (3500/7)*3 = 1500
Working and Sleeping Partners :- A partner who manages the business is known as working partner and the one who simply invest money is a sleeping partner.
Working partner will get profit as well as salary whereas sleeping partner will only get profit no salary.
Lets Understand with an example:-
Example :- A and B started business by investing Rs. 100 and Rs 200 for same period of time but A is a active partner and B is sleeping partner and it was decided that 10 % of salary would be given to A. Find the share of both, out of an annual profit of Rs 30.
Solution :-Annual profit = Rs 30
Salary of A = 10% of 30 = Rs 3.
Now profit = 30 -3 = Rs 27
Now profit is divided into the ratio of capital because both invested for same period of time.
A:B = 100 :200 = 1:2
total ratio = 3
Profit of A = [(1/3)*27 + 3] = 12
Profit of B = (2/3)*27 = 18
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