Here in the concept of partnership, we define partnership as least two people who contribute their cash to carry on a business and share the profits of the business at an agreed proportion.

People who have included in partnership with one another independently are called partners.

## The concept of partnership contains a simple partnership and compound partnership.

### 1.Simple Partnership :

A simple partnership is one in which the capitals of partners are invested for the same amount of time.

### 2. Compound Partnership :

A compound partnership is one within which the capitals of partners are not invested in the same amount of time.

Concept of partnership involves partner who may be Sleeping Partner or Working Partner.

### 1.Sleeping Partner :

Sleeping Partner is the person who puts the capital in the business however does not effectively take part in the conduct of business.

### 2.Working Partner :

Working Partner is the individual who not only invests capital but also takes part in running the business. For his work, he is either paid some compensation or given a specific level of percentage in profit, in addition.

**Useful Formulas Of Partnership Concept :**

- \begin{align*} Profit=Capital\times Time \end{align*}
- Lets us consider two partners A & B invested capitals C1 and C2 for a period of time t1 and t2 respectively then the ratio of their profits is
*Profit of A: Profit of B=*

\begin{align*} \left( C_{1}\times t_{1}\right) :\left( C_{2}\times t_{2}\right) \end{align*} - Lets us consider two partners A & B invested capitals C1 and C2 and their profits are p1 and p2 respectively then
*The ratio of the timing of their individual investments**is*\begin{align*} \left( \dfrac {P_{1}}{C_{1}}\right) :\left( \dfrac {P_{2}}{C_{2}}\right) \end{align*} - If three partners A & B invested their capitals for a period of time t1 and t2 and their profits are P1 and P2 respectively then

*The ratio of their capitals invested is*\begin{align*} \left( \dfrac {P_{1}}{t_{1}}\right) :\left( \dfrac {P_{2}}{t_{2}}\right) \end{align*} - Lets us consider three partners A, B & C invested capitals C1, C2 and C3 for a period of time t1, t2 and t3 respectively then the ratio of their profits is
*Profit of A : Profit of B : Profit of C =*

\begin{align*} \left( C_{1}\times t_{1}\right) :\left( C_{2}\times t_{2}\right) :\left( C_{3}\times t_{3}\right) \end{align*} - Lets us consider three partners A, B & C invested capitals C1, C2 and C3 and their profits are p1, p2 and p3 respectively then
*The ratio of the timing of their individual investments is*

\begin{align*} \left( \dfrac {P_{1}}{C_{1}}\right) :\left( \dfrac {P_{2}}{C_{2}}\right) :\left( \dfrac {P_{3}}{C_{3}}\right) \end{align*} - When three partners A, B & C as partnership invested their capitals for a period of time t1, t2 and t3 and their profits are P1, P2, and P3 respectively then

*The ratio of their capitals invested**is*

\begin{align*} \left( \dfrac {P_{1}}{t_{1}}\right) :\left( \dfrac {P_{2}}{t_{2}}\right) :\left( \dfrac {P_{3}}{t_{3}}\right) \end{align*} - Lets us consider two partners A & B as partnership invested capitals C1 and C2 for the same period and the total profit be Rs.P then
*The shares of partners A and B in the profit are*

\begin{align*} \\ Rs. \left( \dfrac {C_{1}\times P}{C_{1}+C_{2}}\right) and \\ \\ \ Rs. \left( \dfrac {C_{2}\times P}{C_{1}+C_{2}}\right) \\ \\ respectively. \end{align*} - If three partners A, B & C invested capitals C1, C2 and C3 for the same period and the total profit be Rs.P then
*The shares of partners A, B and C in the profit are*

\begin{align*} \\ Rs. \left( \dfrac {C_{1}\times P}{C_{1}+C_{2}+C_{3}}\right) , \\ \\ Rs. \left( \dfrac {C_{2}\times P}{C_{1}+C_{2}+C_{3}}\right) \\ and \\ \\ Rs. \left( \dfrac {C_{3}\times P}{C_{1}+C_{2}+C_{3}}\right) \\ respectively. \end{align*}

- Lets us consider two partners A & B invested capitals C1 and C2 for the periods t1 and t2 respectively and the total profit be Rs.P then
*The shares of partners A and B in the profit are*

\begin{align*} Rs. \left[ \dfrac {C_{1}\times t_{2}\times P}{\left( C_{1}\times t_{1}\right) +\left( C_{2}\times t_{n}\right) }\right] and \end{align*}

\begin{align*} Rs. \left[ \dfrac {C_{2}\times t_{2}\times P}{\left( C_{1}\times t_{1}\right) +\left( C_{2}\times t_{n}\right) }\right] \\ \\ respectively. \end{align*} - Lets us consider three partners A, B & C invested capitals C1, C2 and C3 for the periods t1,t2 and t3 respectively and the total profit be Rs.P then
*The shares of patners A, B and C in the profit are*

\begin{align*} \left[\dfrac {C_{1}\times t_{1}\times P}{\left( C_{1}\times t_{1}\right)+\left( C_{2}\times t_{2}\right)+\left( C_{3}\times t_{3}\right) } \right] , \end{align*}

\begin{align*} \left[ \dfrac {C_{2}\times t_{1}\times P}{\left( C_{1}\times t_{1}\right)+\left( C_{2}\times t_{2}\right)+\left( C_{3}\times t_{3}\right) } \right] \\ and \end{align*} \begin{align*} \left[ \dfrac {C_{3}\times t_{1}\times P}{\left( C_{1}\times t_{1}\right) +\left( C_{2}\times t_{2}\right)+\left( C_{3}\times t_{3}\right) } \right] \\ respectively. \end{align*}