Profit Distribution among Nirmal and Kapil: A Comprehensive Analysis of Business Investments

Businesses frequently face complex situations that require in-depth mathematical analysis to determine profit distribution among partners. In this article, we will explore two scenarios involving Nirmal and Kapil, where the partners invest different amounts at various times during their business journey. We will delve into the calculations needed to accurately allocate the profits.

Scenario 1: Nirmal and Kapil's Initial Investments

Nirmal and Kapil started a partnership with initial investments of Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. At the end of the year, the profit amounted to Rs. 600. How did they share this profit?

Nirmal's investment: 9000 for 12 months 108000

Kapil's investment: 12000 for 6 months 6000 for 6 months 72000 36000 108000

Both Nirmal and Kapil's investments are equivalent, therefore they share the profit equally:

Kapil's share: Rs. 2300

Scenario 2: M and N's Initial Investments and Withdrawal

M and N began their partnership with initial investments of Rs. 12000 and Rs. 16000. After six months, M and N adjusted their investments to Rs. 12000 and Rs. 8000 respectively. Given that their profit after a year was Rs. 5200, how was this profit distributed?

Avg investment of Nirmal: 12000

Avg investment of Kapil: 16000/6 8000/6 13333

The ratio of their investments is:

12000:13333 or 12:13.333

Therefore:

Kapil's share in total profit of Rs. 5200 5200 / 2 * 13333 / 2 Rs 2600

Scenario 3: Capital and Profit Allocation

In this scenario, Nirmal and Kapil invested Rs. 6000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. The total profit at the end of the year was Rs. 4600. How was this profit shared between Nirmal and Kapil?

Calculation Steps:

Initial investments:

Nirmal's initial investment: 6000 for 12 months 72000

Kapil's initial investment: 12000 for 6 months 6000 for 6 months 72000 36000 108000

Ratio of capitals:

72000 : 108000 72 : 108 8 : 12 2 : 3

Total profit: 4600

Kapil's share:

4600 * (3/5) 920 * 3 2760

Conclusion

Understanding the dynamics of business investments and how profits are distributed is crucial for any business owner or partner. These scenarios demonstrate the importance of mathematical calculations in determining fair profit distribution.