When two or more persons join together to carry on a business and agree to share its profits and losses, the arrangement is called partnership.
The persons who invest money in the business are called partners.
Therefore, in partnership problems, the most important quantity is not always the capital alone. The time for which the capital remains invested must also be considered.
If A invests ₹x for t months and B invests ₹y for s months:
A : B = 10,000×12 : 15,000×12
= 10,000 : 15,000
= 2 : 3
When all partners invest their capital for the same period, the profit is divided in the ratio of their capitals.
Profit Ratio = Capital Ratio
Ratio = 20,000 : 30,000 : 50,000
= 2 : 3 : 5
Total parts = 10
A = 20,000 × 2/10 = ₹4,000
B = 20,000 × 3/10 = ₹6,000
C = 20,000 × 5/10 = ₹10,000
If partners invest different amounts for different periods, multiply the capital by the investment time.
A's effective capital = 12,000×8 = 96,000
B's effective capital = 18,000×6 = 108,000
Profit ratio = 96,000 : 108,000
= 8 : 9
A = 16,000×3/8 = ₹6,000
B = 16,000×5/8 = ₹10,000
If a partner joins the business after some months, the capital of that partner is multiplied only by the number of months for which it remains invested.
A's investment = 20,000×12 = 240,000
B's investment = 30,000×8 = 240,000
Therefore:
A : B = 1 : 1
If a partner withdraws the capital before the end of the business period, divide the investment into separate time periods.
A's effective capital = 40,000×12 = 480,000
B's effective capital = 30,000×6 = 180,000
Profit ratio = 480,000 : 180,000
= 8 : 3
When a partner changes the amount of capital during the year, calculate each investment separately.
Effective capital
= 20,000×6 + 30,000×6
= 120,000 + 180,000
= 300,000
For multiple changes, calculate the effective investment of every partner and then compare them.
A working partner actively participates in the management or operation of the business. A sleeping partner generally invests capital but does not actively manage the business.
If the partnership agreement provides a separate salary, commission or other payment to a working partner, that amount is treated according to the conditions given in the question.
Remaining profit = 25,000 − 5,000
= ₹20,000
A's share = 20,000×2/5 = ₹8,000
B's share = 20,000×3/5 = ₹12,000
A's total = 5,000 + 8,000
= ₹13,000
B's total = ₹12,000
A's loss = 18,000×4/9 = ₹8,000
B's loss = 18,000×5/9 = ₹10,000
Sometimes a partner receives a fixed salary before the remaining profit is distributed.
The remaining profit is then distributed according to the specified profit-sharing ratio.
Remaining profit = 50,000 − 5,000
= ₹45,000
A's share = 45,000×3/5 = ₹27,000
B's share = 45,000×2/5 = ₹18,000
A's total = 27,000 + 5,000
= ₹32,000
A partner may receive a commission based on profit. Carefully check whether the commission is calculated before or after the commission itself.
Commission = Profit × Rate / 100
Commission = Profit × Rate / (100 + Rate)
Commission = 40,000×10/100
= ₹4,000
Commission = 40,000×10/110
= ₹3,636.36
When a new partner joins, the new partner contributes capital and usually receives an agreed share of future profits.
C = 1/4
Remaining = 3/4
A = 3/4 × 1/2 = 3/8
B = 3/8
New ratio = 3 : 3 : 2
When a partner retires, the remaining partners continue the business. The new profit-sharing ratio is calculated from the shares retained by the continuing partners.
Remaining partners A and B retain their original shares.
New ratio = 3 : 2
| Situation | Method |
|---|---|
| Same investment period | Compare capital |
| Different investment periods | Capital × Time |
| Capital changes during year | Sum of Capital × Time |
| Fixed salary | Deduct/pay salary as instructed first |
| Commission | Check whether it is before or after commission |
| Concept | Formula / Rule |
|---|---|
| Basic Partnership | Profit Ratio = Capital × Time |
| Two Partners | A : B = C₁T₁ : C₂T₂ |
| Equal Time
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October 12, 2026
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