Simple and Compound Partnerships result when people start a business together or invest in a business. The money or the capital that each partner invests will grow as the company or the business make more and more profit. Consequently, the profit that each partner makes will also change. In this section, you will learn how to calculate the profit or the investment of one or more partners. Let us learn more in the following section!

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## Simple Partnerships

A simple partnership is one in which each of the partners invests a capital sum for the same time. During the tenure of the partnership, all the partners stay. The profits and the losses of each partner can be calculated by noting the initial investments of each of the partners. Let us suppose that a partner A makes a contribution ‘x’ and a partner B makes a contribution ‘y’ in terms of capital investment. Then the formula for the Simple partnerships is:

(Profit of A)/(Profit of B) = x/y

In this way, if we know the profit made by one of the partners, we can calculate the profit of the other partner. Let us see this with the help of an example:

Example 1: Khan and Yawer start a business investing Rs. 169000 and Rs. 130000 respectively. In what ratio should we divide the profit that each of the partners can have?

A) 12 : 13 B) 13 : 10 C) 13 : 31 D) None of these

Answer: This is a simple partnership. The formula for this is (Profit of A)/(Profit of B) = x/y; Following this, we can see that the ratio we are looking for is 169000/130000 = 13/10. Hence the correct option here is B) 13:10.

### Three Partners

Example 2: Three partners start a company and decide to invest a starting amount. Partner A invests Rs. 100000, partner B invests Rs. 200000 and Partner C invests 400000. After one year, the company is worth Rs. 10000000. The shares of the profit of A, B and C are:

A) Rs. 1428571.43, Rs. 2857142, Rs. 4285714.29.

B) Rs. 4285714.29, Rs. 2857142, Rs. 4285714.29,

C) Rs. 67993.21, Rs. 789475.23, Rs. 891838

D) Rs. 982647.32, Rs. 233425, Rs. 672987

Answer: The total profit is Rs. 10000000. Out of this profit, we have to choose each partner’s share. The share will be proportional to the initial investments. The ratio os the initial investments of A, B and C are 1:2:4. Thus the total shares to be distributed are = 1 + 2 + 4 = 7. The profit has to be shared into 7 portions. Thus the value of each portion of the profit = 10000000/7 = Rs. 1428571.43.

Thus the share in the profit for A = Rs. 1428571.43. Similarly the share in the profit of B = 2×Rs. 1428571.43 = Rs. 2857142. Following the same logic, we can see that the profit for C will be = 3×Rs. 1428571.43 = Rs. 4285714.29. Hence the correct option is A) Rs. 1428571.43, Rs. 2857142, Rs. 4285714.29.

## Compound Partnerships

When partners invest money for different time periods, the partnerships are what we call the compound partnerships. Suppose we have two partners A and B who invest an amount of ‘x’ and ‘y’ respectively. Let the partner A be in the partnership for a time of a and let ‘b’ be the time for which the partner B stays in the partnership. The formula for the share of profit = (A’s share of profit)/(B’s share of profit) = x(a)/y(b)

Example 2: Khan and Yawer start another partnership together investing Rs. 100000 and Rs. 50000 respectively. But this time Khan stays in the partnership for three months while Yawer stays in it for an entire year. If the partnership was initially for a year, what is the ratio of their profits?

A) 2 : 1 B) 3 : 2 C) 2 : 3 D) 1 : 2

Answer: As per the question the initial investments of Khan and Yawer are in the ratio 2:1. Using the formula for the compound partnerships, we can write:

(Khan’s share of Profit)/(Yawer’s share of Profit) = (100000×3)/(50000×12); where 12 is the number of months in a year. Thus the ratio of the profits is (Khan’s share of Profit)/(Yawer’s share of Profit) = 1/2 or 1:2. Therefore the ratio is D) 1 : 2.

### Some More Examples

Example 3: Yawer and Khan start a business investing Rs. 84,000 and Rs. 28,000 respectively. The company goes on for 2 years. The ratio in which the profits these partners have earned after two years:

A) 2 : 3 B) 3 : 1 C) 13 : 3 D) None of these

Answer: Let us recall the formula for simple partnerships, (Profit of A)/(Profit of B) = x/y.

Yawer’s share of profit = x where x and y are investments. Khan’s share of profit = y. Therefore, we can write:

x:y = Yawer’s share of profit: Khan’s share of profit

Therefore, (Yawer’s share of profit)/(Khan’s share of profit) = Rs. 84000/Rs. 28000 = 3 : 1

The profit earned after 2 years will be divided between Yawer and Khan in the ratio of 3: 1.

Example 4: In the above example, if the profit of the company after two years is 200000, then what is the profit of each partner?

Answer: Since the profit has to be divided in the ratio 3:1, we divide the profit into 4 shares i.e. 3 + 1. Therefore, we can write 200000/4 = 50000. Thus the profit of Yawer = 50000×3 = Rs. 150000.

Similarly, the profit earned by Khan = 50000×1 = Rs. 50000.

## Practice Questions

Q 1: Raju and Vicki decide to invest in a business. They decide to share the profit in the ratio of 2 : 3. If Raju has invested Rs. 40,000, then what is the investment of Vicki?

A) Rs. 30,000 B) Rs. 45,000 C) Rs. 60,000 D) Rs. 75,000

Ans: C) Rs. 60,000

Q 2: Khan starts a cinema business by investing Rs. 50,000. After six months of doing business, Karim joins Khan’s business with an investment of Rs. 70,000. After 3 years, they both earn a profit of Rs. 25,000. Find Khan’s share of profit.

A) Rs. 13000.00

B) Rs. 13224.65

C) Rs. 12500.50

D) Rs. 11538.46

Ans: D) Rs. 11538.46