Partnership Profit Sharing Ratio: Formula, Rules and Examples
Partnership Profit Sharing Ratio is determined by the capital invested by each partner and the time for which it remains invested. The basic rule is investment multiplied by time. This page explains the partnership profit ratio formula, changing investments, admission or withdrawal of partners, and methods for solving profit sharing questions accurately.
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What Is Partnership Profit Sharing Ratio?
If partners invest capitals C₁, C₂, C₃ for times T₁, T₂, T₃, then their profit-sharing ratio is C₁T₁ : C₂T₂ : C₃T₃. For a total profit P, the first partner's share is P × C₁T₁/(C₁T₁ + C₂T₂ + C₃T₃). Capital must be measured in the same unit and time must be expressed in the same unit for all partners.
Partnership Profit Sharing Ratio Formula & Tricks
Important Formulas
For two or more partners, calculate capital multiplied by time for each partner and compare the resulting values.
P₁ and P₂ are the profit shares, while C and T represent capital and investment time.
Multiply the total profit by the partner's ratio term divided by the sum of all partners' ratio terms.
Divide each profit-ratio term by its corresponding investment time to find the capital ratio.
Quick Tricks
Convert every investment period to the same unit before multiplying. Capital-months can be used when all periods are given in months.
After calculating capital multiplied by time, divide both or all ratio terms by their common factor before distributing profit.
If a partner changes the invested capital, calculate capital-time for each period and add the products.
Partnership Profit Sharing Ratio Concepts
Profit Ratio for Constant Investments
The time factor is common and cancels out. Therefore, if A and B invest ₹40,000 and ₹60,000 for 12 months, their profit ratio is 40,000 : 60,000 = 2 : 3. If the total profit is ₹25,000, A receives ₹10,000 and B receives ₹15,000.
Investment Time Ratio
If A and B invest equal amounts for 9 months and 6 months respectively, their profit ratio is 9 : 6 = 3 : 2. The investment time ratio must use the actual period during which each partner's capital was in the business.
Different Capitals and Different Periods
Suppose A invests ₹20,000 for 9 months and B invests ₹30,000 for 6 months. Their capital-time values are 180,000 and 180,000, so the profit ratio is 1 : 1. Equal capital-time values produce equal profit shares, even when the capital amounts and periods differ.
Changing Capital During the Partnership
A's effective capital-time is the sum of capital multiplied by the duration in each interval. For example, A invests ₹12,000 for 4 months and then ₹18,000 for 8 months: A's value is 12,000 × 4 + 18,000 × 8 = 192,000. This value is then compared with the other partners' capital-time values.
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Partnership Profit Sharing Ratio: Quick Revision
Use these rules to calculate partners' shares and divide the total profit.
- Profit-sharing ratio = Capital × Investment time.
- For constant investments throughout the same period, profit ratio equals capital ratio.
- For equal capitals, profit ratio equals investment time ratio.
- Use the same time unit for every partner, such as months or years.
- If capital changes, split the period and add all capital-time products.
- Individual profit = Total profit × individual ratio part / sum of ratio parts.
- The total of all individual profit shares must equal the total profit.
Partnership Profit Sharing Ratio FAQs
What is the partnership profit ratio formula?
The formula is Profit ratio = Capital invested × Time invested. Thus, for two partners, the ratio is C₁T₁ : C₂T₂.
A invests ₹15,000 for 8 months and B invests ₹20,000 for 6 months. What is their profit ratio?
A's value is 15,000 × 8 = 120,000 and B's value is 20,000 × 6 = 120,000. Therefore, the profit ratio is 1 : 1.
How is a partner's share calculated from a ratio of 3:5?
The ratio total is 8. For total profit P, the partners receive 3P/8 and 5P/8 respectively. If P = ₹16,000, their shares are ₹6,000 and ₹10,000.
What happens when a partner joins after the business starts?
Count the joining partner's capital only from the date of investment. For example, capital C invested for 7 months contributes C × 7 to the profit ratio, not C × 12.
How should a withdrawn investment be treated?
Count the capital only up to the withdrawal date. If capital C remains invested for t months before withdrawal, its contribution to the ratio is C × t.
Can profit shares be equal when investment amounts are different?
Yes. Equal profit shares result when capital-time products are equal. For example, ₹20,000 for 9 months and ₹30,000 for 6 months both give a capital-time value of ₹180,000.