Partnerships Explained | Types & Profit Sharing

When two or more people come together to start a business, it is called a partnership. The money invested by them is known as capital, and typically, partners share profits or losses in proportion to their investments. Let’s dive into the essentials of partnerships, including types, profit-sharing mechanisms, and examples to enhance your understanding.

Types of Partners

1. Managing Partners: These are active participants involved in the day-to-day activities of the business.
2. Sleeping Partners: These partners contribute capital but do not take part in the operational activities.

Profit Sharing in a Partnership

Problems involving profit sharing can be categorized into three main cases:

Case 1: Equal Time Period Investment

When all partners invest their capital for an equal time period, profits or losses are shared in the ratio of their invested capital.

Example: If A, B, and C invest ₹5000, ₹10,000, and ₹20,000 respectively, profits will be shared in the ratio 5:10:20.

Case 2: Unequal Time Period Investment

When partners invest capital for different time periods, profits are divided in the ratio of the product of their capital and time period.

Formula: Profit ratio = Capital × Time

Example: If A invests ₹10,000 for 6 months, B invests ₹20,000 for 3 months, and C invests ₹30,000 for 2 months, profits are shared in the ratio 60:60:60 or 1:1:1.

Case 3: Working vs. Sleeping Partners

In partnerships with both working and sleeping partners, there are two approaches:

1. Working partners draw a fixed salary based on their contribution.
2. Working partners receive an additional share of profits.

Example: If A and B invest equally but A manages the business, they may agree to a 60:40 profit-sharing ratio to compensate for A’s effort.

Sample Problems with Solutions

Question 1: A and B invest in a business in the ratio 4:2. If 4% of the total profit goes to charity and A’s share is ₹845, what is the total profit?

Solution:

1. Total profit after charity = ₹100 (assuming total profit = ₹100).
2. A’s share = 95 × (4/6) = ₹63.33.
3. Total profit = ₹100 when A’s share = ₹63.33.
4. Total profit = (100/63.33) × 845 = ₹1334.28.

Question 2: A, B, and C invest in a business for 6 months, 5 months, and 3 months respectively. The profit earned is ₹7200. Calculate B’s share if A receives 5% for managing.

Solution:

1. A’s managing share = 5% of ₹7200 = ₹360.
2. Remaining profit = ₹7200 – ₹360 = ₹6840.
3. Profit ratio = (6500 × 6):(8400 × 5):(10,000 × 3) = 39:42:30 = 13:14:10.
4. B’s share = ₹6840 × (14/37) = ₹2588.11.

Question 3: X, Y, and Z invest in the ratio 7:4:3. After 4 months, X increases his share by 60%. If the total profit is ₹20,500, what is Y’s share?

Solution:

1. Initial investment ratio = 7:4:3.
2. Adjusted ratio = (7 × 4 + 60% of 7 × 8): (4 × 12): (3 × 12) = 98:40:45.
3. Total ratio = 183.
4. Y’s share = ₹20,500 × (40/183) = ₹4480.87.

Conclusion

Understanding partnerships, including their types, key concepts, and profit-sharing methods, is essential for anyone involved in business ventures. By clearly defining roles and responsibilities and agreeing on profit distribution, partnerships can be highly successful. With proper planning and communication, partnerships offer opportunities for growth and shared success.