Compound Partnership: Formula, Examples and Questions
Compound Partnership problems distribute profit among partners whose investments may differ in amount and duration. The profit ratio is calculated by multiplying each partner’s capital by the time for which it remains invested. This page covers the compound partnership formula, changing investments, profit distribution, solved examples and useful calculation methods.
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What Is Compound Partnership?
For each partner, calculate the capital-time product: Capital × Time. Use the same time unit for every partner, usually months. The resulting products are simplified to obtain the profit ratio. For example, if A invests ₹5,000 for 12 months and B invests ₹8,000 for 9 months, their ratio is 5,000 × 12 : 8,000 × 9 = 60,000 : 72,000 = 5 : 6.
Compound Partnership Video Lessons
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Partnership: Simple vs Compound Investment
Understand how simple and compound investments differ in partnership problems, including the calculation of individual contributions, investment duration, and profit-sharing proportions.
Compound Partnership Formula & Tricks
Important Formulas
Multiply each partner’s invested capital by the time it remains in the business, then simplify the products.
The partner’s capital-time product is divided by the total of all partners’ products.
When capital changes during the year, calculate a separate capital-time product for each period and add them.
Unless the agreement states otherwise, losses are divided in the same ratio as profits.
Quick Tricks
Cancel common factors before multiplying large numbers. This reduces calculation time and avoids unnecessary arithmetic.
Treat every capital change as a separate investment period. Add the products for the same partner before comparing ratios.
Months, years and days cannot be mixed directly. Convert them to a common unit before forming the ratio.
Compound Partnership Concepts
Profit Sharing with Different Capitals and Times
Calculate each partner’s capital-time product and simplify the resulting ratio. If A invests ₹4,000 for 9 months and B invests ₹6,000 for 6 months, then A:B = 4,000 × 9 : 6,000 × 6 = 36,000 : 36,000 = 1:1.
Profit Share from a Given Total Profit
For a ratio of 5:6:3 and total profit ₹28,000, the total parts are 14. The shares are ₹28,000 × 5/14 = ₹10,000, ₹28,000 × 6/14 = ₹12,000, and ₹28,000 × 3/14 = ₹6,000.
Capital Changed During the Partnership
Suppose A invests ₹6,000 for 12 months. B invests ₹9,000 for 4 months and ₹12,000 for the next 8 months. A’s product is 72,000, while B’s product is 9,000 × 4 + 12,000 × 8 = 132,000. Therefore, A:B = 72:132 = 6:11.
Joining or Leaving the Partnership
If A invests ₹10,000 for 12 months and B joins with ₹15,000 for 8 months, the ratio is 10,000 × 12 : 15,000 × 8 = 120,000 : 120,000 = 1:1. A partner who leaves early is similarly counted only up to the withdrawal date.
Salary, Commission and Interest Adjustments
If total profit is ₹50,000 and A receives a salary of ₹5,000, the remaining ₹45,000 is distributed according to the partnership ratio. If a commission is given as a percentage of profit, apply the stated percentage first according to the question’s conditions.
Compound Partnership Data Table
Use the structured data below while following the explanation and examples.
Capital-time calculation for three partners
The table shows how capital and time produce the compound partnership ratio.
| Partner | Capital (₹) | Time (months) | Capital × Time | Simplified ratio |
|---|---|---|---|---|
| A | 5,000 | 12 | 60,000 | 5 |
| B | 8,000 | 9 | 72,000 | 6 |
| C | 6,000 | 6 | 36,000 | 3 |
Note: The capital-time products 60,000:72,000:36,000 simplify to 5:6:3.
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Compound Partnership Revision Points
Use these formulas and rules to solve compound partnership problems.
- Profit ratio = Capital × Time for each partner.
- Use the same time unit for all partners before forming the ratio.
- For a changing capital, add the capital-time products of each period.
- A partner who joins or leaves is counted only for the actual investment period.
- Individual profit = Total profit × individual ratio part ÷ total ratio parts.
- Salary, commission or interest is adjusted before dividing the balance when the question specifies it.
- Losses normally follow the same capital-time ratio as profits.
Compound Partnership FAQs
What is the compound partnership formula?
Profit ratio = (Capital × Time) for each partner. Thus, the ratio is formed by multiplying every partner’s capital by the period for which it is invested.
A invests ₹12,000 for 8 months and B invests ₹16,000 for 6 months. What is their profit ratio?
A:B = 12,000 × 8 : 16,000 × 6 = 96,000:96,000 = 1:1.
How is profit calculated when a partner changes capital during the year?
Calculate each period separately and add the products. For ₹10,000 invested for 5 months and ₹15,000 for 7 months, the effective product is ₹50,000 + ₹105,000 = ₹155,000.
How are years and months compared in compound partnership?
Convert them into the same unit. One year equals 12 months, so 1 year and 9 months represent 12 months and 9 months, respectively.
What is the difference between simple and compound partnership?
In simple partnership, the capital ratio is used when the investment period is the same. In compound partnership, both capital and investment time are considered.
A and B have a profit ratio of 3:5 and earn ₹32,000. What are their shares?
Total parts = 8. A receives ₹32,000 × 3/8 = ₹12,000, and B receives ₹32,000 × 5/8 = ₹20,000.