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 working partner. Some other important points associated with partnership are given below.
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.
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).
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.
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.
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?
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.
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
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.
P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)
= 95 : 95 : 90
= 19 : 19: 18
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.
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
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.
Let P’s capital = p, Q’s capital = q and R’s capital = r
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
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
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000