Partnership is something in which a formal agreement is made between two or more people and agree to become co-owners, distribute the responsibilities for running an organization, and share the profits made in that business. Or share the loss. In government recruitment examination, many questions related to partnership are asked. While solving questions, you may get confused on the correct formula and tricks to apply to get the answer. In this post, we are going to discuss important formulas related to partnership with examples. This study notes will help you to solve questions related to this topic easily.

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**What is partnership?**

Whenever two or more persons join hands with the same objective to achieve benefits. So each member contributes time or cash, allowing the organization to benefit.

The partner who invests only the money * passive partner *It is said that a partner who invests the money and also manages the business is called

*It is said. Some other important points related to the partnership are given below.*

**active partner****Partnership or types of partnerships****,**

There are two types of partnerships as simple and mixed partnerships. Details of both types of partnerships are given below.

**Simple Partnership:**

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In this type of partnership, resources i.e. capital (or other resources) are invested by all the investors for the same time period and all the capital remains in the business during that period. In such partnerships, profits are distributed in proportion to their contributed capital.

**Formula**

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

**Profit (or loss) of P : Profit (or loss) of Q = a : b**

**mixed partnership**

In compound partnerships, money is invested by different investors for different periods of time. In this, the profit margin is calculated by multiplying the capital invested and time (usually months).

**Formula**

**P1 : P2 = C1 × T1 : C2 × T2**

- P1 = first partner’s profit
- C1 = First partner’s capital
- T1 = Time period of amount invested by the first partner
- P2 = Profit of second partner
- C2 = Second partner’s capital
- T2 = Time period of amount invested by the second partner

**Important Points:**

**1**, When the investments of all the partners are for the same period of time, the profit or loss is distributed among the partners in proportion to their investments.

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

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

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

Let A invest Rs. x. B invests Rs.y for p months and B invests Rs. y for q months. So,

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

**Question:**

**1. Three partners shared profits in a business in the ratio 5:7:8. They were in partnership for 14 months, 8 months and 7 months respectively. Then what will be the ratio of the capital invested by them?**

A. 5 : 7 : 8

B. 20 : 49 : 64

C. 38 : 28 : 21

D. None of these

**Ans. (B)**

**Explanation:**

Let their investment be Rs. x for 14 months, Rs. y for 8 months. And for 7 months z Rs. Is.

So, 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.

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

**2. P, Q, R form a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4, After two months, P withdraws half of the capital and after 10 months, Rs. 378 If the profit of Rs is divided among all, then what will be Q’s share in it?**

A.114

B.120

C.134

D.144

**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 invest Rs 50,000 for a business. Contribute. A borrows Rs 4000 from B. More and B contributes Rs 5000 more than C. So 35,000, Rs. How much amount will A get in total profit?**

A.Rs. 8400

B.Rs. 11,900

C.Rs. 13,600

D.Rs. 14,700

**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. P, Q, R form a partnership. P initially invests 25 lakhs and after one year invests another 10 lakhs. Q withdraws Rs 35 lakh initially and Rs 10 lakh after 2 years and R invests Rs 30 lakh. So in what ratio the profit should be divided at the end of 3 years?**

A. 18:19:19

B.18:18:19

C.19:19:18

D.18:19:19

**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 by investing Rs 20,000 and Rs 15,000 respectively. After six months, C joined them with Rs 20,000. So at the end of 2 years from the start of the business the profit is Rs 25,000. What will be B’s share in the total profit?**

A.Rs. 7500

B.Rs. 9000

C.Rs. 9500

D.Rs. 10,000

**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, while the ratio between the amounts invested by A and B was 3 : 2. If their total profit was Rs 157300, then what amount did B receive?**

A.48000

B.48200

C.48400

D.48600

**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, C rent a pasture. A keeps 10 bulls for 7 months; B keeps 12 oxen for 5 months and C keeps 15 oxen for 3 months. If the rent of pasture is Rs 175. , then how much will C have to pay as his share of the rent?**

A.Rs. 45

B.Rs. 50

C.Rs. 55

D.Rs. 60

**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, what amount will R receive?**

A.600

B.700

C.800

D.900

**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, C start a business. B’s capital is four times C’s capital; And the capital of A is equal to three times the capital of B. If the total profit at the end of one year is Rs 16500, then find the share of B in it.**

A.4000

B.5000

C.6000

D.7000

**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 is divided in the ratio 2:3. If P had invested Rs 40000, what is the amount invested by Q?**

A.40000

B.50000

C.60000

D.70000

**Ans(C)**

**Explanation:**

Let the amount invested by Q = q

40000 : q = 2 : 3

=> 40000/q = 2/3

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

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