Description
The chapter “Partnership Business” from the Class 10 Mathematics curriculum under the West Bengal Board of Secondary Education (WBBSE) deals with how profits or losses are shared among business partners based on their respective investments and durations. This chapter is rooted in practical arithmetic, introducing students to the fundamentals of profit-sharing ratios, capital contribution, and time-based variations in a business partnership. It also covers changing investments and entries/exits of partners during the business period.
1. What is a Partnership Business?
A partnership business is a form of business structure where two or more individuals invest capital to run a business and agree to share the profit or loss. The share of each partner depends primarily on two factors:
- The amount of capital invested
- The duration of the investment
This chapter teaches how to calculate each partner’s share using basic ratio and proportion methods.
2. Key Concepts and Terms
2.1 Capital Contribution
This refers to the amount of money each partner invests into the business. Larger investments usually entitle a partner to a larger share of the profit.
Example:
If Partner A invests ₹10,000 and Partner B invests ₹15,000, then their capital ratio is 2:3.
2.2 Duration of Investment
Sometimes, partners invest for different periods. In such cases, profit is distributed based on “Capital × Time” for each partner.
Example:
- Partner A invests ₹6,000 for 10 months
- Partner B invests ₹8,000 for 6 months
Their effective investments are: - A: 6,000 × 10 = 60,000
- B: 8,000 × 6 = 48,000
So, profit is shared in the ratio 60,000 : 48,000 = 5:4
2.3 Ratio of Profit Sharing
This is the simplified ratio of the product of each partner’s investment and time.
Formula:
Partner’s Share = (Capital × Time) of that partner / Total (Capital × Time) of all partners
3. Types of Partnership Situations
3.1 Simple Partnership
All partners invest their capital at the same time for the same duration.
Example:
- A and B invest ₹5,000 and ₹10,000 respectively
- Duration: 1 year (same)
Capital ratio = 1:2 ⇒ Profit is shared in 1:2 ratio
3.2 Time-Based Partnership
Partners invest different amounts for different durations. The profit is divided based on capital × time.
Example:
- A: ₹12,000 for 8 months ⇒ 96,000
- B: ₹15,000 for 6 months ⇒ 90,000
Profit ratio = 96,000 : 90,000 = 16:15
3.3 Changing Partners / Entry & Exit
When a new partner joins or an existing partner leaves during the business term, their contribution is counted only for their respective time duration.
Example:
- A and B start a business
- C joins after 4 months with ₹9,000
- Calculate profit based on each partner’s active time and capital invested
4. Profit and Loss Distribution
4.1 Calculating Individual Share in Profit
Step 1: Calculate each partner’s investment multiplied by their respective time
Step 2: Find the total of all (capital × time)
Step 3: Divide the total profit in that ratio
Example:
- A: ₹5,000 for 12 months ⇒ 60,000
- B: ₹6,000 for 10 months ⇒ 60,000
Total = 1,20,000
If total profit = ₹24,000
Each gets half: ₹12,000
4.2 Distribution in Case of Loss
The process is the same for loss as for profit. The total loss is shared based on the same ratio.
5. Important Formulas
- Investment Ratio = Capital of A : Capital of B (if time is same)
- Effective Investment = Capital × Time
- Partner’s Share = (Partner’s Effective Investment / Total Effective Investment) × Total Profit or Loss
6. Practical Examples
Example 1 – Simple Partnership:
A and B invest ₹20,000 and ₹30,000 respectively in a business. After one year, the profit is ₹25,000.
Capital ratio = 2:3
Profit share:
- A = (2/5) × 25,000 = ₹10,000
- B = (3/5) × 25,000 = ₹15,000
Example 2 – Time-Based Investment:
A invests ₹10,000 for 12 months, B invests ₹15,000 for 8 months
Effective investment:
- A = 10,000 × 12 = 1,20,000
- B = 15,000 × 8 = 1,20,000
Equal share of profit if profit = ₹36,000 ⇒ ₹18,000 each
7. Application in Real Business
This concept is widely used in:
- Small businesses where friends or family invest together
- Startups with staggered investor entry
- Business partnerships involving unequal investment durations
Understanding partnership calculations allows for fair and transparent distribution of earnings or losses among stakeholders.
8. Summary
The Partnership Business chapter introduces learners to real-world business arithmetic, emphasizing the fair division of profits and losses. Key concepts include:
- Sharing profits in proportion to investment and time
- Calculating individual shares using ratios
- Adjusting for changing investments or timeframes
Applying formulas like Capital × Time to find effective shares