Partnership – Complete Short Notes for Competitive Exams

1. Basic Concept

Partnership problems are based on sharing profit or loss according to capital contribution and time.

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

$Share of Partner A = \frac{A’s Capital × Time}{Sum of (Capital × Time of all partners)} \times Total Profit$

4. Equal Time Investment

If all partners invest for same duration:

Profit ratio=Capital ratio

Example: A:B = 2:3 → profit shared = 2:3

5. Unequal Time Investment

If investment periods differ:

Profit ratio=Capital × Time ratio

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

If a partner joins after some time, his investment counts only for the period invested.
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

If a partner withdraws before the business ends, time reduces his share proportionally.
Use same Capital × Time formula.

8. Mixed Investments (Different Capitals & Times)

Multiply Capital × Time for each period of investment.
Add contributions for multiple periods per partner.
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

Profit is shared according to new agreed ratio
If profit of old partners for past months known, subtract old partner shares to calculate new partner’s share.

10. Goodwill

New partner may pay goodwill for joining
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

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