Points to Remember:
- Partnership profit sharing.
- Calculation of individual shares based on a given ratio and salary.
- Application of ratio and proportion principles.
Introduction:
This question involves a basic partnership problem where profits are distributed based on a pre-agreed ratio, with one partner receiving a salary in addition to their share of the remaining profit. Partnerships are common business structures where individuals pool resources and share profits and losses. The distribution of profits often hinges on pre-defined agreements, which can include fixed salaries for working partners and profit-sharing ratios based on investment, contribution, or other factors. This problem requires us to use simple arithmetic and ratio calculations to determine the individual profit shares of each partner.
Body:
1. Determining the Profit after A’s Salary:
A receives â¹3 lakh in total. This includes his salary (10% of the total profit) and his share of the remaining profit. Let’s denote the total profit as ‘x’. A’s salary is 0.1x. The remaining profit is x – 0.1x = 0.9x.
A’s total earnings are given as â¹3 lakh. This is the sum of his salary and his share of the remaining profit. His share of the remaining profit is (2/9) * 0.9x = 0.2x (since the remaining profit is distributed in the ratio 2:3:4, and A’s share is 2 out of 9 parts).
Therefore, we can set up the equation: 0.1x + 0.2x = 300000
Solving for x: 0.3x = 300000 => x = 1000000
The total profit is â¹10 lakh.
2. Calculating Individual Shares:
- A’s Salary: 10% of â¹10 lakh = â¹1 lakh
- A’s Share of Remaining Profit: (2/9) * â¹9 lakh = â¹2 lakh
- A’s Total Earnings: â¹1 lakh + â¹2 lakh = â¹3 lakh (This confirms our calculation)
- B’s Share of Remaining Profit: (3/9) * â¹9 lakh = â¹3 lakh
- C’s Share of Remaining Profit: (4/9) * â¹9 lakh = â¹4 lakh
3. Summary of Earnings:
| Partner | Salary | Share of Remaining Profit | Total Earnings |
|—|—|—|—|
| A | â¹1,00,000 | â¹2,00,000 | â¹3,00,000 |
| B | â¹0 | â¹3,00,000 | â¹3,00,000 |
| C | â¹0 | â¹4,00,000 | â¹4,00,000 |
Conclusion:
The total profit of the business is â¹10 lakh. After deducting A’s salary of â¹1 lakh, the remaining â¹9 lakh is distributed among the partners A, B, and C in the ratio 2:3:4. Therefore, B receives â¹3 lakh, and C receives â¹4 lakh. This problem highlights the importance of clearly defined profit-sharing agreements in partnerships to ensure fairness and transparency among partners. A well-structured partnership agreement, clearly outlining salary provisions and profit-sharing ratios, is crucial for the long-term success and stability of any business partnership. This approach ensures equitable distribution and minimizes potential conflicts among partners.