Overview: Partnership | Quantitative Techniques for CLAT PDF Download

In Partnerships, we study the business partners and their deals. The business started by two or more parties is often governed by an agreement or a contract. We call these business contracts the partnerships. Partnerships govern the division of profit and loss of a business. In the following sections, we have the different concepts that we require to study partnerships and deduce the scales of profit and loss.

Simple and Compound Partnerships

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.

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
Ans: (b)
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.

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
Ans: (a)
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 3: 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
Ans: (d)
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.

Working and Sleeping Partners

In many businesses, you will see that the partner that is working is called working partner. While the other partner is sleeping or he is silent so he is called sleeping partner. The sleeping partner only invests the money, he does not do any managerial work or administrative work. He is not involved in the day to day works of the company. The working partner manages the business and hence get paid in the form of salary or remuneration for it. While the profit is being distributed, the salary part has to be met first, any profit remaining after this can be divided on the basis of the ratio of the partner’s investment.

Example 4: Raghav, Rahul, and Roma started a business with an investment of Rs. 12 lakhs, 8 lakhs, and 5 lakhs respectively. Raghav and Rahul are also working as CEO and Director. They get a fixed monthly salary of Rs. 37,000 and Rs. 28,000 respectively out of the profit that the company makes. Find out the earnings of Roma. The company makes the profit the of 21 lacs at the end of the year.
(a) Rs. 2,64,000
(b) Rs. 2,55,000
(c) Rs. 2,66,000
(d) Rs. 2,70,000
Ans: (a)
From the question, you can derive that Raghav and Rahul are the working partners. Thus they will also be compensated with the fixed salary every month besides their shares in the profit. While Roma is the silent partner. She will only get her part of profit based on the ratio of her investment.
The share of investment of Raghav, Rahul, and Roma is 12: 8: 5. So, the share of Roma’s profit will be 5/25. But before calculating her share we need to deduct the yearly salaries of Raghav and Rahul.
Raghav’s yearly salary: (37000 x 12) = Rs. 4,44,000
Rahul’s yearly salary: (28000 x 12)
= Rs. 3,36,000
Thus, remaining profit after the deduction of their salaries will be, 21 – (4.44 + 3.36) = Rs. 13.2 lakhs.
So, Roma’s share will be, (5/25 x 13.2) = Rs. 2,64,000. Thus, the correct answer is (a).

Ratio of the Division of Gains

Profits are what govern a partnership. A contract or a deal by which two or more investors or parties come together is known as a partnership agreement. The agreement tells us how to split Profits and loses. The partners usually agree to some set rules and proceed with the business or the proposal.

Division of Profits

A business or a company is successful when it is making profits. There are many businesses which are run by the multiple people called partners. And each and every partner have invested different amounts. Based on this the profits are divided. Usually, there are two types of scenarios in which profits of the company are divided. They are:

• When the investments are done for a different time period then the equivalent amount is calculated for that unit of time by having (capital x number of units of time). Thus, the profit or loss made is divided in the ratio of these capitals. Suppose, X invests Rs. a for ‘m’ months and Y invests Rs. b for ‘n’ months, then it will be calculated as,
  (X’s share of profit/loss) : (Y’s share of profit/loss) = am : bn
  
• When the investments done by all the partners for the equal amount of time, the profit or loss will be distributed between the partners in the ratio of their investments. Suppose X and Y invest Rs. a and Rs. b respectively for a period of 1 year in a startup then at the end of that year the profit/loss will be calculated as:
  (X’s share of profit/loss) : (Y’s share of profit/loss) = a : b.
• Using the above formulas we will solve different types of questions. Based on these questions, there are also practice questions for you at the end.

Examples of three partners

Example 5: Ram started a business by investing Rs. 90,000. After 3 months, Shyam joined Ram and invested the amount of Rs. 120,000. After another 6 months, Mahesh joined both of them by investing Rs. 180,000. It was found that the profit made by all of them at the end of the year was Rs. 33,000. What was the share of each person?
Sol: The given question is based on the 1st type that can be asked in the exam. In this question, the three people mentioned have invested in three different time periods. So, from the question you can see that Ram has invested his amount for 12 months, Shyam has done it for 9 months, and Mahesh has invested his amount for 3 months.
So, based on the time period and the amount invested by each of the members, the ratio will be,
(90000 x 12) : (120000 x 9) : (180000 x 3)
⇒ 1080000 : 1080000 : 540000
⇒ 108 : 108 : 54 = 18 : 18 : 3 = 2 : 2 : 1
So, we can see that Ram will 2 parts as his share, Shyam will have 2 parts as his share, and Mahesh will have 1 part as his share.
Thus, the share of each person will be as follows:
Ram’s share: (33000 x 2/5) = Rs. 13,200
Shyam’s share: (33000 x 2/5) = Rs. 13,200
Mahesh’s share: (33000 x 1/5) = Rs. 6600

Examples of two partners

Example 6: Ramesh started his television business with an initial investment of Rs. 35 crores. He was joined by Suresh after 5 months with an investment of Rs. 27 crores. Together they made a profit of Rs. 145 crores. Find out Suresh’s share.
Sol: As the time period of investment of Ramesh and Suresh is different, their share in the profit will also be different. First, we need to find out the ratio of their investment. The ratio for the profit sharing between Ramesh and Suresh will be (35 x 12) : (27 x 7) = 20: 9.
Based on the above ratio we need to divide profit into 20: 9.
So, Suresh’s profit will be: (145 x 9/29) = Rs. 45 crores.

Data Sufficiency

Partnership conditions are the terms under which a partnership is created. In partnerships, the questions from data sufficiency are a very common occurrence in the competitive exams. They can be asked from any chapters. And thus today our topic for data sufficiency will be on partnership conditions.

Partnership Conditions

We have covered several topics on partnerships in our previous articles. And so today we are going to show you to solve the questions based on partnership conditions in data sufficiency. So, we will look into some of the common questions asked under this section. Before solving the questions, here are the directions for the questions:

Each question given will be followed by two statements.
(a) if statement I alone is sufficient, but statement II alone is not sufficient.
(b) if statement II alone is sufficient, but the statement I alone is not sufficient.
(c) if both the statements I and II together are sufficient, but neither statements alone is sufficient.
(d) if each statement alone is sufficient.
(e) if statement I and II together are not sufficient.

Example 7: Three friends named Ram, Shyam and Mukesh started a business together. What was Shyam’s overall profit at the end of the year?
The statement I: Mukesh invested Rs. 8000 for the 1st 9 months. Mukesh’s investment was 4 times as much as of Ram and 3/2 times that of Shyam.
Statement II: The investment done by Ram and Shyam was in the proportion of 1: 2 in one year.
Statement III: The total profit at the end of the year was Rs. 1000.
(a) Only 1st and 2nd statement
(b) Only 1st and 3rd statement
(c) All of these
(d) None of the statements
(e) The information given in the statements is insufficient.
Ans: (d)
As there are three statements given in the question, we need to solve it on the basis of the options. So, on combining 1st and 2nd statement, we get,
Total money invested by Mukesh = (8000 x 9) = Rs. 72000.
Total money invested by Ram = (1/4 x 8000 x 12) = Rs. 24000
All the money invested by Shyam = (3/2 x 72000) = Rs. 48000
So, the ratio of the money invested by all of them will be 72000: 48000: 24000 = 3: 2: 1. So, we have found the ratio of each individual but we need to find the share of their profit. Thus, a statement I and II alone cannot be sufficient to determine the answer.
Furthermore, in the third statement, the total amount of profit is given. So, the share of Shyam’s profit will be (1/3 x 1000) = Rs. 333. 33.
So the correct answer is option (d).