### Maths Partnership

##### What is a Partnership?

A partnership is a legal entity formed by two or more individuals, called partners, who agree to carry on a business together and share the profits and losses. There are several types of partnerships, each with its own characteristics and legal implications. Here are some common types of partnerships:

##### Types of Partnerships

The type of partners who only finance money are included under the sleeping partner and a partner who sponsors funds as well as manages the business is named the working partner. Based on this there are two types of partnerships; simple partnerships and compound partnerships.

##### Simple Partnership

In this type of partnership, all the resources are sponsored for the same period by all the investors. May it be the capital or other resources. Also, the profit is circulated as per the contribution of the resources. The simple partnership formula is discussed below:

##### Simple Partnership Formula

If we consider X and Y as two contributors who contribute P and Q amount respectively for a year in a particular business, then their profit or loss earned at that time will be:

$$\text{X’s profit or loss : Y’s profit or loss} = P : Q$$

##### Compound Partnership

As the name suggests in such a partnership, the money is funded during distinct periods by numerous investors. Also, the benefit-sharing ratio is confirmed by replicating the capital contributed with the unit of time.

##### Compound Partnership Formula

The compound partnership formula is as follows:

$$X1 : X2 = Y1 × Z1 : Y2 × Z2$$

Where,

- $X1$ = 1’st partners’ earnings.
- $Y1$ = 1’st partners investment.
- $Z1$ = time for which 1’st partner contributed his money.
- $X2$ = 2’nd partners earnings.
- $Y2$ = 2’nd partners investment.
- $Z2$ = time for which 2’nd partner contributed his money.

##### Relation between Profit and Capital

Candidates can find the relationship between profit and capital from below.

Profit (P) is proportional to Capital (C). Therefore, the ratio of profits P1 and P2 is equal to the ratio of capitals C1 and C2:

$$P1 : P2 = C1 : C2$$

Also, check out the concepts of percentages once you are through with partnership concepts!

##### Change in Capital

In this type of partnership problem, the capital value changes over time.

##### Rent Distribution

In this type of partnership problem, the rent is distributed among the available people by following a ratio.

##### Condition Dependent

In this type of partnership problems, the question consists of some predefined conditions.

##### How to Solve Question Based on Partnership – Know all Tips and Tricks

Candidates can find different tips and tricks from below for solving the questions related to partnership.

**Tip #1:** Candidates need to make sure that they know all the important formulas of partnership which are mentioned below.

- Profit is proportional to investment.
- Profit is proportional to time.
- Profit (P) is proportional to Capital (C).

Therefore, the ratio of profits P1 and P2 is equal to the ratio of capitals C1 and C2:

$$P1 : P2 = C1 : C2$$

**Tip #2:** The first two formulas shall be applied only when the Time Period is the same or constant.

##### Partnership Solved Sample Questions

##### Question 1:

A partnership firm consists of three partners, A, B, and C. Their capital contributions are in the ratio of 3:2:1. The total profit of the firm for the year is Rs. 1,80,000. Calculate the share of each partner in the profit.

**Solution:**

Given that,

Capital contribution ratio of A : B : C = 3 : 2 : 1

Let their capital contributions be 3x, 2x, and x respectively.

Therefore, total capital = 3x + 2x + x = 6x

Now, profit sharing ratio = Capital contribution ratio

Therefore, A’s share of profit = (3x/6x) * 1,80,000 = Rs. 90,000

B’s share of profit = (2x/6x) * 1,80,000 = Rs. 60,000

C’s share of profit = (x/6x) * 1,80,000 = Rs. 30,000

**Hence, A’s share of profit is Rs. 90,000, B’s share of profit is Rs. 60,000, and C’s share of profit is Rs. 30,000.**

##### Question 2:

A partnership firm has two partners, X and Y. Their capital contributions are in the ratio of 2:3. The firm earns a profit of Rs. 1,20,000 for the year. Calculate the interest on capital for each partner if the interest rate is 10% per annum.

**Solution:**

Given that,

Capital contribution ratio of X : Y = 2 : 3

Let their capital contributions be 2x and 3x respectively.

Therefore, total capital = 2x + 3x = 5x

Now, interest on capital for X = (2x/5x) * 10% * 1,20,000 = Rs. 48,000

Interest on capital for Y = (3x/5x) * 10% * 1,20,000 = Rs. 72,000

**Hence, the interest on capital for X is Rs. 48,000 and the interest on capital for Y is Rs. 72,000.**

##### Question 3:

A partnership firm has three partners, A, B, and C. Their capital contributions are in the ratio of 5:3:2. The firm suffers a loss of Rs. 60,000 for the year. Calculate the share of each partner in the loss.

**Solution:**

Given that,

Capital contribution ratio of A : B : C = 5 : 3 : 2

Let their capital contributions be 5x, 3x, and 2x respectively.

Therefore, total capital = 5x + 3x + 2x = 10x

Now, loss sharing ratio = Capital contribution ratio

Therefore, A’s share of loss = (5x/10x) * 60,000 = Rs. 30,000

B’s share of loss = (3x/10x) * 60,000 = Rs. 18,000

C’s share of loss = (2x/10x) * 60,000 = Rs. 12,000

**Hence, A’s share of loss is Rs. 30,000, B’s share of loss is Rs. 18,000, and C’s share of loss is Rs. 12,000.**