Simple Partnership: Formula, Examples and Questions

Simple Partnership deals with dividing profit or loss among partners who invest different amounts of capital for the same period. The share of each partner is proportional to the capital invested. This page covers the simple partnership formula, common solving methods, numerical examples and practice-based questions.

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What Is Simple Partnership?

Simple partnership is a business arrangement in which all partners invest capital for the same duration, so profit or loss is divided in the ratio of their capital investments.

If partners invest capitals A, B and C for the same period, their profit-sharing ratio is A:B:C. For a total profit P, the share of a partner investing capital C is P × C ÷ (sum of all capitals). For example, if A and B invest ₹4,000 and ₹6,000, their profit ratio is 4:6 = 2:3.

Simple 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.

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Simple Partnership Formula & Tricks

Important Formulas

Profit-sharing ratio
Profit ratio = Capital of A : Capital of B

When all partners invest for the same period, profit or loss is divided in the ratio of their capitals.

Individual profit share
Partner's share = Total profit × Partner's capital ÷ Total capital

Use this formula to calculate the amount received by one partner.

Total profit or loss
Total profit or loss = Sum of all partners' shares

The individual shares must add up to the total profit or loss.

Capital from profit share
Capital of a partner = Total capital × Partner's profit share ÷ Total profit

This rearranged formula finds an unknown capital when the total capital and profit shares are known.

Quick Tricks

Reduce the capital ratio first

Convert the capital amounts into their lowest ratio before dividing the profit. This reduces the calculation.

Example: Capitals ₹12,000 and ₹18,000 give the ratio 12:18 = 2:3. A profit of ₹25,000 is divided into 5 parts, so the shares are ₹10,000 and ₹15,000.
Use one ratio part

After finding the profit ratio, divide the total profit by the sum of ratio parts. Multiply the result by each partner's ratio number.

Example: For a ratio of 3:5 and profit of ₹16,000, one part is ₹16,000 ÷ 8 = ₹2,000. The shares are ₹6,000 and ₹10,000.
Loss follows the same ratio

In a simple partnership, a loss is distributed using the capital ratio, just like profit.

Example: If capitals are in the ratio 4:1 and the loss is ₹5,000, the partners bear ₹4,000 and ₹1,000 respectively.

Simple Partnership Concepts

Profit Sharing Using Capital Ratio

For equal investment periods, the profit-sharing ratio is equal to the ratio of the partners' capitals.

Let A, B and C invest ₹a, ₹b and ₹c respectively. Then their shares of profit are in the ratio a:b:c. If the total profit is P, A's share is P × a ÷ (a + b + c).

Example: A and B invest ₹20,000 and ₹30,000. Their ratio is 2:3. If the profit is ₹15,000, A receives ₹6,000 and B receives ₹9,000.

Finding an Individual Partner's Share

An individual share is found by multiplying the total profit by that partner's capital and dividing by the total capital.

First calculate total capital. Then apply Partner's share = Total profit × Partner's capital ÷ Total capital. The same method applies when there are three or more partners.

Example: A, B and C invest ₹5,000, ₹7,000 and ₹8,000. For a profit of ₹10,000, B's share is ₹10,000 × 7,000 ÷ 20,000 = ₹3,500.

Finding Capital from Profit Shares

When the profit shares are given, the partners' capitals are in the same ratio as those shares.

If A and B receive ₹4,000 and ₹6,000, their capitals are in the ratio 4:6 = 2:3. If one capital is known, use the ratio to calculate the other capital.

Example: A and B share profit in the ratio 3:5. If A invests ₹12,000, B's capital is ₹12,000 × 5 ÷ 3 = ₹20,000.

Distribution of Loss

A business loss is divided among simple partners in the same ratio as their capital investments.

If the capital ratio is a:b:c and the total loss is L, the partners' losses are La ÷ (a+b+c), Lb ÷ (a+b+c) and Lc ÷ (a+b+c). A loss is treated as a negative profit for calculation.

Example: A, B and C invest in the ratio 2:3:5. For a loss of ₹20,000, their losses are ₹4,000, ₹6,000 and ₹10,000.

Simple Partnership Data Table

Use the structured data below while following the explanation and examples.

Simple Partnership Profit Allocation

Profit of ₹24,000 divided according to the capital ratio of three partners.

Partner Capital Capital ratio Profit share
A ₹10,000 2 ₹4,800
B ₹15,000 3 ₹7,200
C ₹25,000 5 ₹12,000
Total ₹50,000 10 ₹24,000

Note: The capital ratio is 10:15:25 = 2:3:5. One ratio part equals ₹24,000 ÷ 10 = ₹2,400.

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Practice Simple Partnership Questions

Practise published questions related to this topic.

110 2/3 + 15 1/3 - 4 1/6 = ?→ 2An article was sold at a loss of 12%. If it was sold for ₹ 630 more, then there would have been a gain of 6%. Find the cost price of the article.→ 3A product is sold at 25% profit. If the cost price is 240, find the selling price.→ 4If 20% of a number is added to 84, then the result is the same number. 70% of the same number is:→ 5Find the value of x in the given expression. x/2.1 + 4.2/6.3 = 4→ 6A grocery store gives a Buy 5, Get 2 Free offer. The price of each item is ₹300. A customer needs a total of 21 items and procures the items under this scheme. What is the effective cost per item? (Round off your answer to two decimal places.)→ 7The LCM of the numbers 1.3, 7.6 and 0.13 is:→ 8The fraction equivalent to 9.90909... is:→ 9Simplified form of (3√15 × 2√5)/(5√3) is→ 1073 + 92 - 61 + (41 + 21) - 78 + 33 = ?→

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Quick Revision Notes

Simple Partnership Revision Points

Key rules and formulas for quick revision.

  • For equal time periods, profit or loss ratio equals the capital ratio.
  • Profit share = Total profit × Individual capital ÷ Total capital.
  • Reduce capital amounts to the lowest ratio before dividing profit.
  • The sum of all individual shares must equal the total profit or loss.
  • If profit shares are known, the capital ratio is the same as the profit-share ratio.
  • Simple partnership assumes that all partners invest for the same duration.

Related Topic Explainers

Partnership with Change in Investment → Equivalent Ratios → Comparing Ratios → Scaling Ratios → K Method in Ratio and Proportion →

Simple Partnership FAQs

What is the simple partnership formula?

For equal investment periods, Profit ratio = Capital ratio. An individual partner's share is Total profit × Partner's capital ÷ Total capital.

A and B invest ₹8,000 and ₹12,000. How is a profit of ₹5,000 divided?

Their capital ratio is 8:12 = 2:3. Therefore, A receives ₹2,000 and B receives ₹3,000.

How is a loss divided in simple partnership?

The loss is divided in the ratio of the partners' capitals. For capitals in the ratio 3:2 and a loss of ₹10,000, the losses are ₹6,000 and ₹4,000.

If A and B share profit in the ratio 4:5, what is their capital ratio?

Their capital ratio is also 4:5, provided both partners invested for the same period.

A, B and C invest ₹6,000, ₹9,000 and ₹15,000. What is B's share of a ₹12,000 profit?

The capital ratio is 2:3:5, with 10 total parts. B receives ₹12,000 × 3 ÷ 10 = ₹3,600.

A invests ₹15,000 and receives ₹6,000 from a profit shared in the ratio 2:3. What is B's capital?

A's ratio part is 2, so B's capital is ₹15,000 × 3 ÷ 2 = ₹22,500.

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