CAT Partnership: Two or more persons involved in a partnership - Practice Questions & MCQ

In the context of quantitative aptitude, partnership primarily relates to the distribution of profit or loss among partners based on their investment and the duration of their investment.

Definition:

Partnership: It is an association of two or more persons who invest their money, labour, and skills in a business and share its profit and losses in a proportionate manner.

Key Formula:

1. If two or more persons invest their capital in a business for the same period of time, then the profit or loss is divided among them in the ratio of their investments.

2. If they invest their capitals for different lengths of time, then the profit or loss is distributed in the ratio of their capital-time (also called 'capital-months').

Foundation Building Questions:

Question:

A and B entered into a partnership investing Rs. 50,000 and Rs. 60,000 respectively. After 4 months, A withdraws half of his capital. At the end of the year, a total profit of Rs. 21,000 was earned. How will the profit be shared between A and B?

Solution:

First, calculate the capital-months for both A and B.

For A: 

For the first 4 months, capital = Rs. 50,000.

For the next 8 months, capital = Rs. 50,000/2 = Rs. 25,000.

Total capital-months for A = (50,000 x 4) + (25,000 x 8) = 2,00,000 + 2,00,000 = 4,00,000.

For B: 

Capital remains unchanged = Rs. 60,000.

Total capital-months for B = 60,000 x 12 = 7,20,000.

The ratio of their capital-months = 4,00,000:7,20,000 = 5:9.

Profit for A = (5/14) x 21,000 = Rs. 7,500.

Profit for B = (9/14) x 21,000 = Rs. 13,500.

Tips and Tricks:

1. Determine the Time: Always check if the capital investment time is the same for all partners. If not, calculate capital-months.

2. Ratio is Crucial: Most partnership problems revolve around determining the correct ratio in which the profit or loss will be shared.

3. Stay Organised: When dealing with multiple partners and varying amounts/times, tabulate the data. This will help in avoiding confusion and mistakes.

4. Combine with Ratio Concepts: As seen in the solution, combining the understanding of ratios can simplify the profit distribution calculation.

5. Wordings are Important: Pay attention to words like "withdraw", "additional investment", etc., as they change the conditions of the problem.

6. Practise Different Variations: Partnership problems can come with various twists – e.g., introduction of a new partner, death of a partner, etc. Familiarise yourself with these scenarios.

Partnership problems are often considered tricky because they combine elements of ratio and proportion, time, and arithmetic operations. However, with systematic approaches and continuous practice, students can easily solve even complex partnership questions.