Minakshi started a business investing â¹45,000. After 3 months, Anil joined her with â¹60,000, and after another 6 months, Sunil joined with â¹90,000. At the end of the year, they made a profit of â¹16,500. Find the share of each.

Points to Remember:

This is a problem of profit sharing based on investment and time.
The share of profit is directly proportional to the product of investment and time period.

Introduction:

This question involves calculating the profit share of three partners in a business based on their individual investments and the duration of their involvement. Profit sharing in a partnership is governed by the agreement between the partners. In the absence of a specific agreement, profits are typically shared in proportion to the capital contributed by each partner. However, when the investment periods differ, the calculation becomes more complex, requiring consideration of both capital invested and the time for which it was invested.

Body:

1. Calculating Investment-Time Products:

To determine the share of each partner, we need to calculate the product of their investment and the duration of their investment.

Minakshi: Invested â¹45,000 for 12 months (the entire year). Investment-time product = 45,000 * 12 = 540,000
Anil: Invested â¹60,000 for 9 months (from month 4 to month 12). Investment-time product = 60,000 * 9 = 540,000
Sunil: Invested â¹90,000 for 6 months (from month 7 to month 12). Investment-time product = 90,000 * 6 = 540,000

2. Total Investment-Time Product:

The total investment-time product is the sum of the individual investment-time products: 540,000 + 540,000 + 540,000 = 1,620,000

3. Calculating Individual Profit Shares:

Each partner’s share of the profit is proportional to their investment-time product relative to the total investment-time product.

Minakshi’s share: (540,000 / 1,620,000) * â¹16,500 = â¹5,500
Anil’s share: (540,000 / 1,620,000) * â¹16,500 = â¹5,500
Sunil’s share: (540,000 / 1,620,000) * â¹16,500 = â¹5,500

Conclusion:

In this scenario, despite differing investments and investment periods, Minakshi, Anil, and Sunil each receive an equal share of the â¹16,500 profit â â¹5,500 each. This is because their investment-time products are equal. This highlights the importance of considering both the amount of investment and the duration of the investment when calculating profit shares in a partnership. For future partnerships, a clear and well-defined profit-sharing agreement should be established upfront to avoid potential disputes. This agreement should clearly outline the contribution of each partner, the duration of their involvement, and the method of profit distribution, ensuring fairness and transparency. This approach promotes a sustainable and equitable business environment, aligning with principles of fair business practices.

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