Partnership

Partnership is one of the most important arithmetic topics in Quantitative Aptitude. Questions from this chapter are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.

Partnership problems are based on the sharing of profit or loss among two or more persons who jointly invest money in a business for a certain period of time.

This chapter is directly connected with:

• Ratio and Proportion
• Percentage
• Profit and Loss
• Simple Interest
• Time and Work

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What is Partnership?

When two or more persons invest money in a business and share profit or loss according to their investments and investment duration, such an association is called:

The persons involved in the business are called:

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Basic Concepts of Partnership

1. Investment

The amount invested by a partner in the business is called:

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2. Time Period

The duration for which money remains invested in the business is called:

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3. Profit Sharing

Profit or loss is distributed among partners according to:

✔ Profit sharing in partnership is always proportional to the product of capital and time.

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Important Formula of Partnership

If:

• A invests x for p months
• B invests y for q months

Then:

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Case 1: Same Time Investment

If all partners invest money for the same duration, then profit sharing ratio is directly proportional to their investments.

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Case 2: Different Time Investment

If partners invest for different durations, then:

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Types of Partnership

1. Simple Partnership

If partners invest:

• Different capitals for same time
• OR same capital for different time

Then such partnership is called:

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2. Compound Partnership

If partners invest:

• Different capitals
• AND different time periods

Then such partnership is called:

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Types of Partners

1. Active or Working Partner

A partner who:

• Invests money
• Participates in business activities
• May receive salary or bonus

Such a partner is called:

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2. Sleeping Partner

A partner who:

• Only invests money
• Does not participate in business activities

Such a partner is called:

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Important Partnership Formulae

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How to Solve Partnership Problems?

1. Identify each partner's investment.
2. Identify the investment duration.
3. Multiply capital by time.
4. Form the profit-sharing ratio.
5. Distribute total profit according to ratio.

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Partnership with Admission of New Partner

Sometimes a new partner joins the business after a certain time.

In such cases:

• Calculate separate investment periods.
• Use capital × time for each partner.
• Find the final ratio.

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Partnership with Salary or Commission

Sometimes an active partner receives:

• Salary
• Commission
• Bonus

These amounts are deducted from total profit before distribution.

✔ Salary or commission is deducted first, remaining profit is divided according to partnership ratio.

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Important Concepts for Competitive Exams

1. Profit Depends on Two Things

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2. Same Investment Period

If time is same:

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3. Same Investment Amount

If investment amount is same:

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Common Mistakes in Partnership

• Ignoring investment duration.
• Incorrect multiplication of capital and time.
• Forgetting to deduct salary or commission.
• Errors in ratio simplification.
• Using wrong time units.

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Important Exam Tips

• Always use Capital × Time method.
• Convert years into months whenever necessary.
• Simplify ratios carefully.
• Practice admission and withdrawal cases regularly.
• Remember salary deduction concept.
• Verify calculations before final answer.
• Use ratio method for faster calculations.

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Quick Formula Revision

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Partnership is one of the easiest and most scoring chapters in Quantitative Aptitude. Strong understanding of capital-time relationships and ratio calculations helps candidates solve partnership problems quickly and accurately in competitive examinations.