When more than one person agree to invest their money to run a business or firm then this kind of agreement is called partnership. The persons involved in the partnership are called partners.

There are two types of partners.

1. Sleeping Partner: Sleeping partner is the person who provides only investment but does not take part in running the business.
2. Working Partner: Working partner is the person who not only invests the money but also takes part in running the business. For this work he is paid some salary or some percent of profit in addition.

There are two types of partnership.

1. Simple Partnership:  In simple partnership, capitals of partners are invested for the same period of time.
2. Compound Partnership:  In compound partnership, capitals of partners are invested for the different period of time.

## Basic Formulas of Partnership

If two partners A and B are investing their money to run a business then
(Simple Partnership)

Capital of A : Capital of B = Profit of A : Profit of B

If two partners A and B are investing their money for different period of time to run a business then
(Compound Partnership)

Capital of A × Time period of A : Capital of B × Time period of B = Profit of A : Profit of B

Example

Jack and Jill start a business by investing \$ 2,000 for 8 months and \$ 3,000 for 6 months respectively. If their total profit si \$ 510 and then what is profit of Jill?
Sol:

Capital of Jack = 2000 and Time period = 8 months
Capital of Jill = 3000 and Time period = 6 months

So, Profit of Jack : Profit of Jill = 8 : 9
So we have 8 + 9 = 17 parts of total profit.
Out of this 17 parts, Jack will get 8 parts and Jill will get 9 parts.

Now, total profit is 510
So, One Part = 510/17 = 30.

Jill’s profit = 30 × 9 = 270 and
Jack’s profit = 30 × 8 = 240.

If n partners are investing for different period of time then

C1T1 : C2T2 : C3T3 : … : CnTn = P1 : P2 : P3 : … : Pn

Where C is the capital invested, T is time period of capital invested and P is profit earned.

Example

Raju, Kamal and Vinod start a business by investing Rs 5,000 for 12 months, Rs 8,000 for 9 months and Rs 10,000 for 6 months. If at the end of the year their total profit is Rs 2000 then find the profit of each partner.
Sol:

Raju’s investment is 5000 for 12 months.
Kamal’s investment is 8000 for 9 months.
Vinod’s investment is 10000 for 6 months.

So their ratio of investments is
5000 × 12 : 8000 × 9 : 10000 × 6
60 : 72 : 60
5 : 6 : 5

So their profit,
Raju : Kamal : Vinod = 5 : 6 : 5

So there are 5 + 6 + 5 = 16 parts of profit.
Out of these 16 parts, Raju will get 5 parts, Kamal will get 6 parts and Vinod will get 5 parts.

So, Total profit = 2000
One part = 2000/16 = 125

Raju’s profit = 5 × 125 = 625
Kamal’s profit = 6 × 125 = 750
Vinod’s profit = 5 × 125 = 625

## Shortcut Methods for Partnership

Rule 1:

If two partners are investing their money C1 and C2 for equal period of time and their total profit is P then their shares of profit are

If these partners are investing their money for different period of time which is T1 and T2, then their profits are

Example

Jack and Jill start a business by investing \$ 2,000 for 8 months and \$ 3,000 for 6 months respectively. If their total profit si \$ 510 and then what is profit of Jill?
Sol:

Let’s Say C1 = 2000, T1 = 8
C2 = 3000, T2 = 6
P = 510

Rule 2:

If n partners are investing their money C1, C2, …, Cn for equal period of time and their total profit is P then their shares of profit are

If these partners are investing their money for different period of time which is T1, T2,… , Tn then their profits are

Example

Raju, Kamal and Vinod start a business by investing Rs 5,000 for 12 months, Rs 8,000 for 9 months and Rs 10,000 for 6 months. If at the end of the year their total profit is Rs 2000 then find the profit of each partner.
Sol:

Let’s Say C1 = 5000, T1 = 12
C2 = 8000, T2 = 9
C3 = 10000, T3 = 6
P = 2000