Partnership – Complete Short Notes for Competitive Exams
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1. Basic Concept
Partnership problems are based on sharing profit or loss according to capital contribution and time.
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Total capital contributed by each partner and the duration of investment determines share of profit or loss.
2. Key Terms
| Term | Meaning |
|---|---|
| Capital | Money invested by a partner |
| Time/Duration | Number of months or years money is invested |
| Share of Profit | Proportional to (Capital × Time) |
| Total Profit | Sum of profits shared among partners |
3. Fundamental Formula
4. Equal Time Investment
If all partners invest for same duration:
Profit ratio=Capital ratio
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Example: A:B = 2:3 → profit shared = 2:3
5. Unequal Time Investment
If investment periods differ:
Profit ratio=Capital × Time ratio
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Example:
A invests ₹5000 for 12 months → 5000×12 = 60,000
B invests ₹8000 for 6 months → 8000×6 = 48,000
Profit ratio = 60,000 : 48,000 = 5:4
6. Partner Joins Late
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If a partner joins after some time, his investment counts only for the period invested.
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Formula remains: Capital × Time
Example
A invests ₹10,000 for 12 months
B invests ₹12,000 for 8 months
Profit ratio = (10,000×12) : (12,000×8) = 1,20,000 : 96,000 = 5:4
7. Partner Leaves Early
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If a partner withdraws before the business ends, time reduces his share proportionally.
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Use same Capital × Time formula.
8. Mixed Investments (Different Capitals & Times)
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Multiply Capital × Time for each period of investment.
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Add contributions for multiple periods per partner.
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Then share profits proportionally.
Example:
A invests ₹5000 for 6 months, then ₹2000 more for 6 months
B invests ₹6000 for 12 months
A’s total contribution = (5000×6) + (7000×6) = 30,000 + 42,000 = 72,000
B = 6000×12 = 72,000
Profit ratio = 72,000 : 72,000 = 1:1
9. Addition of a New Partner
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Profit is shared according to new agreed ratio
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If profit of old partners for past months known, subtract old partner shares to calculate new partner’s share.
10. Goodwill
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New partner may pay goodwill for joining
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Goodwill is divided among old partners in profit ratio
Example:
A:B profit ratio = 2:3
C joins, pays ₹50,000 goodwill
A gets 2/5 × 50,000 = 20,000
B gets 3/5 × 50,000 = 30,000
11. Loss Sharing
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Loss is shared like profit, in proportion to capital contribution or agreed ratio.
12. Shortcut/Quick Formulas
| Concept | Formula |
|---|---|
| Share of Profit | (Capital × Time) / Sum(Capital × Time)×Total Profit |
| Equal time | Profit ratio = Capital ratio |
| Joining late / leaving early | Multiply capital by effective months invested |
| Goodwill | Paid by new partner, divided among old partners by ratio |
| Loss sharing | Same as profit, proportional to capital or agreed ratio |
13. Practice Examples
Q1. A invests ₹5,000 for 12 months, B invests ₹8,000 for 6 months. Total profit = ₹6,600. Share?
A : B = 60,000 : 48,000 = 5:4 → Total 9 parts
A = 5/9 × 6600 = ₹3,666.67
B = 4/9 × 6600 = ₹2,933.33
Q2. A invests ₹10,000, B invests ₹15,000. Profit = ₹5,000. Share?
Profit ratio = 10,000 : 15,000 = 2:3
A = 2/5 × 5000 = ₹2,000
B = 3/5 × 5000 = ₹3,000
Q3. C joins, pays ₹25,000 goodwill, old partners A:B = 3:2. Share?
A = 3/5 × 25,000 = ₹15,000
B = 2/5 × 25,000 = ₹10,000
14. Real-life Applications
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Business profit/loss sharing
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Investment planning
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Partnership accounting
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Dividend sharing in joint ventures
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Financial exams and aptitude tests
✅ One-Line Summary
“In partnership, profit or loss is shared proportionally to Capital × Time unless agreed otherwise.”
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