Cheatsheet: Partnership | Cheatsheets for Bank Exams PDF Download

Introduction

A Partnership is a business arrangement in which two or more individuals or entities share the profits and liabilities of the business. In quantitative aptitude, partnership problems generally involve distributing profits or losses among partners based on their contributions in terms of money and time.

Theory

Basic Concept of Partnership:

1. Capital Contribution: The amount of money invested by each partner.

2. Time Contribution: The time for which each partner’s capital remains invested.

3. Profit or Loss Distribution: The share of profit or loss each partner gets is directly proportional to their product of capital and time.

   • Formula for Share of Profit/ Loss:

   • Share of a Partner = (Capital of the Partner × Time for which Capital was Invested) / Total of (Capital × Time) of all partners

Important Formulas

1. Share of Profit or Loss:

• Share of a Partner = (Capital of Partner × Time of Investment) / Total of (Capital × Time) of all Partners

2. Combined Profit or Loss of Multiple Partners:

If there are multiple partners, the combined profit or loss can be divided as:

• Total Profit or Loss = Σ [(Capital × Time) / Total Capital × Time]

3. Relation between Amount, Capital, and Time:

For a partner with capital C1 and time T1, and a second partner with capital C2 and time T2, the amount for both will be:

• C1 × T1 / C2 × T2 This ratio determines their share in the partnership.

4. Partnership Problems Involving Interest:

If the problem includes interest, the formula will also involve the time for which the capital is invested and the rate of interest.

Tips for Solving Partnership Problems

1. Understand the Contributions:

• Read the problem carefully to identify the capital invested by each partner and the time for which it was invested.

• Calculate the product of capital and time for each partner.

2. Time and Capital are Key:

• In problems where the capital is different for each partner, and the time for which they invested is different, remember to calculate the "Capital × Time" for each partner.

3. Simplify the Calculation:

• If the problem involves multiple partners, calculate the total sum of all the "Capital × Time" values. Then, use it to determine the share of each partner.

4. Use Proportions:

• Partnership problems are often based on ratios. Convert the problem into a ratio form, and then solve it using basic ratio concepts.

5. Follow the Profit or Loss Split:

• Once you calculate the total share of each partner, use it to divide the total profit or loss according to the ratio derived from their capital-time contribution.

6. Watch for Special Cases:

• Some problems may include additional complexities such as varying profit-sharing ratios, loans, or changes in capital at different times. Carefully adjust the capital-time values accordingly.

Conclusion

Partnership problems are straightforward once you understand the key concepts of capital, time, and profit-sharing. The most important formula is the calculation of each partner’s share based on the product of capital and time. Remember to always pay attention to the time of investment, especially if it changes during the course of the problem. By following the tips and using the formulas, you can quickly and accurately solve partnership-related questions.

This cheatsheet should help you efficiently tackle partnership problems in your quantitative aptitude preparation.