Partnerships

Master partnership calculations for RRB exam preparation with comprehensive concepts and practice problems.

Basic Concepts

Partnership Definition

What is Partnership?

• Business Association: Two or more persons investing together
• Profit Sharing: Distributed based on investment and time
• Risk Sharing: All partners share business risks
• Agreement: Usually written, can be oral

Types of Partnerships

• Simple Partnership: Same investment duration for all partners
• Compound Partnership: Different investment durations
• Limited Partnership: Some partners have limited liability

Key Terms

Capital Investment

• Initial Investment: Money invested by each partner
• Additional Investment: Extra money invested during business
• Total Investment: Sum of all investments
• Effective Investment: Investment × Time period

Profit Distribution

• Profit Sharing Ratio: Based on effective investment
• Loss Sharing: Same ratio as profit sharing
• Interest on Capital: Sometimes included in calculations

Important Formulas

Simple Partnership

• Profit Ratio = Investment of Partner A : Investment of Partner B
• Share of Profit = (Partner’s Investment ÷ Total Investment) × Total Profit

Compound Partnership

• Effective Investment = Investment × Time Period
• Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂) : …
• Share of Profit = (Effective Investment ÷ Total Effective Investment) × Total Profit

Partnership with Time

• When partners join at different times:
  • Calculate effective investment for each partner
  • Use compound partnership formula

Special Cases

Sleeping Partner

• Invests capital but doesn’t actively participate
• Usually gets less profit share
• May receive fixed interest instead

Working Partner

• Actively participates in business
• May get extra profit for services
• May receive salary in addition to profit share

Practice Problems

Question 1

A and B invest ₹20,000 and ₹30,000 respectively in a business. If the total profit is ₹25,000, find A’s share.

Question 2

A invests ₹15,000 for 3 months and B invests ₹25,000 for 6 months. Find their profit-sharing ratio.

Question 3

Three partners A, B, and C invest ₹10,000, ₹15,000, and ₹25,000 respectively. If the total profit is ₹50,000, find B’s share.

Question 4

A and B start a business with investments of ₹12,000 and ₹8,000 respectively. After 4 months, A withdraws half his investment. Find their profit-sharing ratio.

Question 5

X invests ₹50,000 for the entire year, Y invests ₹40,000 for 6 months, and Z invests ₹60,000 for 4 months. If the total profit is ₹1,20,000, find X’s share.

Question 6

A and B invest in the ratio 3:5. If B’s share of profit is ₹15,000, find the total profit.

Question 7

Two partners invest ₹25,000 each for different periods. A invests for 8 months and B for 12 months. Find A’s share if total profit is ₹22,000.

Question 8

A, B, and C invest ₹4,000, ₹6,000, and ₹8,000 respectively. A is a working partner and gets 10% extra profit for managing the business. If total profit is ₹33,000, find B’s share.

Question 9

A and B start a business with investments of ₹15,000 and ₹10,000 respectively. After 3 months, C joins with ₹20,000. Find their profit-sharing ratio at the end of the year.

Question 10

Three partners invest ₹24,000, ₹36,000, and ₹48,000 respectively. The working partner gets 20% extra profit. If the total profit is ₹1,40,000 and A is the working partner, find B’s share.

Solution Methods

Step-by-Step Approach

Simple Partnership Problems

1. Identify investments of all partners
2. Calculate profit-sharing ratio
3. Apply ratio to total profit
4. Find individual shares

Compound Partnership Problems

1. Calculate effective investment (Investment × Time)
2. Find profit-sharing ratio from effective investments
3. Distribute profit according to ratio
4. Consider any special conditions (working partner, etc.)

Working Partner Calculations

1. Calculate regular profit share
2. Add extra percentage/amount for working partner
3. Distribute remaining profit among all partners
4. Ensure total profit distribution matches total profit

Important Notes

Key Points to Remember

1. Time Period: Consider when partners join/leave
2. Investment Changes: Account for additional/withdrawn capital
3. Working Partners: May receive extra compensation
4. Profit Sharing: Always proportional to effective investment

Common Mistakes

1. Ignoring Time: Forgetting to multiply investment by time
2. Wrong Ratios: Incorrectly calculating profit-sharing ratios
3. Extra Deductions: Not accounting for working partner’s extra share
4. Partial Periods: Incorrectly calculating time periods

Quick Tips

1. Check Logic: Partner with more investment/time gets more profit
2. Verify Totals: Sum of individual shares should equal total profit
3. Simplify Ratios: Always reduce ratios to simplest form
4. Units: Ensure all investments are in same units

Advanced Problems

Multiple Investment Changes

• Account for different investment amounts at different times
• Calculate separate effective investments for each period
• Sum up effective investments for total calculation

Retirement/Admission

• Retirement: Calculate retiring partner’s share up to retirement date
• Admission: Calculate new partner’s share from admission date
• Goodwill: Consider goodwill adjustments when partners change

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