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A partnership is something where a formal agreement between two or more people is made and agreed to be the co-owners, distribute responsibilities for running an organization and share the income or losses that the business generates. In government recruitment exams, many questions are asked related to the partnership. While solving the questions, you might get confused about the right formula and tricks to apply to get the answer. In this post, we are going to discuss the important formulas related to the partnership along with examples. The study notes will help you solve the questions related to this topic easily.

**What is a Partnership?**

Whenever two or more people join hands with the same objective to achieve benefits. Each member contributes either time, cash, or licenses to enable the association firm to harvest benefits.

The partner who only invests money is called a ** Sleeping Partner **and a partner who invests money and also manages the business is called the

**. Some other important points associated with partnership are given below.**

*working partner***Types of Partnerships:**

There are two types of partnership in the form of simple and compound partnerships. The details of both types of partnerships are given below.

**Simple Partnership**

In Simple partnerships, all the resources are invested for the same time period by all the investors i.e. the capital (or other resources) stays in the business for the same duration. In this, the profit is distributed in proportion of their contributed resources.

**Formula**

If P and Q contributed Rs. a and b respectively for one year in business, then their profit or loss at that time will be:

**P’s benefit (or misfortune) : Q’s profit(or misfortune) = a : b**

**Compound Partnership**

In a compound partnership, the money is invested during different periods of time by multiple investors. The benefit-sharing proportion is ascertained by duplicating the capital contributed with the unit of time (generally months).

**Formula**

**P1 : P2 = C1 × T1 : C2 × T2**

- P1 = Partner 1’s Profit.
- C1 = Partner 1’s Capital.
- T1 = Time period for which Partner 1 contributed his capital.
- P2 = Partner 2’s Profit.
- C2 = Partner 2’s Capital.
- T2 = Time period for which Partner 2 contributed his capital.

**Important Formulas**

**1**. When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.

For example, A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

**(A’s share of profit) : (B’s share of profit) = x : y.**

**2. **When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.

Suppose A invests Rs. x for p months and B invests Rs. y for q months then,

**(A’s share of profit) : (B’s share of profit)= xp : yq.**

**Questions**

**1. Three partners shared the profit in a business in the ratio 5: 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investments?**

**Ans. (B)**

**Explanation:**

Let their investments be Rs. x for 14 months, Rs. y for 8 months, and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now, 14x/8y = 5/7 => 98x = 40y => y = 49/20 x

And, 14x/7z = 5/8 => 112x = 35z => z = 112/35 x = 16/5 .x.

So x : y : z = x : 49/20 x : 16/5 x = 20 : 49 : 64.

**2. P, Q, and R enter into a partnership & their share are in the ratio of 1/2: 1/3: 1/4, after two months, P withdraws half of the capital & after 10 months, a profit of Rs 378 is divided among them. What is Q’s share?**

**Ans. (D)**

**Explanation :**

The ratio of their initial investment = 1/2: 1/3: 1/4

= 6 : 4: 3

Let’s take the initial investment of P, Q and R as 6x, 4x and 3x respectively

A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12

= (12+30) : 4*12 : 3*12

=(4+10) : 4*4 : 12

= 14 : 16 : 12

= 7 : 8 : 6

B’s share = 378 * (8/21) = 18 * 8 = 144

**3. A, B, C subscribe to Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:**

**Ans (D)**

**Explanation:**

Let C = x.

Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.

So, x + x + 5000 + x + 9000 = 50000

=> 3x = 36000

=> x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

So A’s share = Rs. (35000 x 21/50) = Rs. 14,700.

**4. 29. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs. In what ratio should the profit be divided at the end of 3 years?**

**Ans (C)**

**Explanation :**

P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)

= 95 : 95 : 90

= 19 : 19: 18

**5. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B’s share in a total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?**

**Ans (A)**

**Explanation:**

A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.

So B’s share = Rs. (25000 x 3/10) = Rs. 7,500.

**6. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?**

**Ans (C)**

**Explanation :**

Assume that investment of C = x

Then, investment of A =2x

Investment of B = 4x/3

A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3

B’s share = 157300 * 4/(6+4+3) = 157300*4/13

= 12100*4 = 48400

**7. A, B, and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?**

**Ans (A)**

**Explanation:**

A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.

C’s rent = Rs.(175 x 9/35) = Rs. 45.

**8. If 4 (P’s Capital ) = 6 ( Q’s Capital ) = 10 ( R’s Capital ), then out of the total profit of Rs 4650, R will receive**

**Ans (D)**

**Explanation :**

Let P’s capital = p, Q’s capital = q and R’s capital = r

Then

4p = 6q = 10r

=> 2p = 3q = 5r

=>q = 2p/3

r = 2p/5

P : Q : R = p : 2p/3 : 2p/5

= 15 : 10 : 6

R’s share = 4650 * (6/31) = 150*6 = 900

**9. Three partners A, B, and C start a business. B’s Capital is four times C’s capital and twice A’s capital is equal to thrice B’s capital. If the total profit is Rs 16500 at the end of a year, Find out B’s share in it.**

**Ans (C)**

**Explanation :**

Suppose C’s capital = x then

B’s capital = 4x (Since B’s Capital is four times C’s capital)

A’s capital = 6x ( Since twice A’s capital is equal to thrice B’s capital)

A:B:C =6 x : 4x : x

= 6 : 4 : 1

B’s share = 16500 * (4/11) = 1500*4 = 6000

**10. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is**

**Ans (C)**

**Explanation :**

Let the amount invested by Q = q

40000 : q = 2 : 3

=> 40000/q = 2/3

=> q = 40000 * (3/2) = 60000