Ratio of the Division of Gains: Profits, Solved & Practice Questions

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. There are many different types of questions from partnership asked in the exam.

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:

1. 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

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2. 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.

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Examples of three partners

Q. 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?

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

Q. 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.

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.

Practice questions:

Q. Amit, Sumit, and Chand entered into a partnership by investing 1500, 2500, and 3000 rupees respectively. Amit was a manager and gets one-tenth of the profit, while the remaining profit is divided among the three in the ratio of their investment. If Amit’s total share is Rs. 369. What will be the share of Sumit?

A. Rs. 420, Rs. 490 B. Rs. 500, Rs. 480
C. Rs. 410, Rs. 486 D. Rs. 405, Rs. 486

The correct answer is D.

Q. In a partnership between A, B, and C, A invests Rs. 2000. If in a profit of Rs. 1600, A’s share is Rs. 400 and C’s share is Rs. 200, then what was the amount that B invests?

A. Rs. 6000 B. Rs. 5000 C. Rs. 6500 D. Rs. 3000

The correct answer is B.

Q. Three partners X, Y, and Z invested Rs. 1600, Rs. 1800, and Rs. 2300 respectively in a business. How should they divide the profit of Rs? 399?

A. Rs. 112, Rs. 128, Rs. 159
B. Rs. 112, Rs. 126, Rs. 161
C. Rs. 110, Rs. 126, Rs. 163
D. Rs. 112, Rs. 128, Rs. 159

The correct answer is B.

Q. In a business Mohit, Azhar, and Sachin invested their capital in the ratio of 3 : 3: 6. If the total profit was Rs. 10,000 then was the share of profit between Mohit and Sachin?

A. Rs. 2500 B. Rs. 2000 C. Rs. 2700 D. Rs. 2600

The correct answer is A.

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