Profit Proportional Investments and Joining Periods

In the realm of small business and entrepreneurial ventures, understanding the dynamics of profit sharing and investment timing is crucial. This article delves into the specific scenario where two parties, A and B, invest in a business under varying conditions. We will explore the underlying mathematics to determine at what point B joined the venture and how the profits are shared. We'll also examine a similar scenario involving another pair of investors, M and S, to further solidify the principles involved.

Scenario 1: A and B

A invested Rs 36000 in a business for a full year. After a few months, B joined with Rs 14000. The total profit was divided between them in the ratio 2:1 at the end of the year. We need to find out after how many months B joined.

To solve this, we start by calculating A's total investment over the year:

Investment by A 36000 * 12 432000

Let B's total investment be x. Since the profit sharing is proportional to investments, we have:

432000 : x 2 : 1

From this, we can determine x as follows:

x 432000 / 2 216000

Next, we calculate the number of months B invested:

216000 / 5400 5 months

Therefore, B joined after 12 - 5 7 months of A's joining.

Scenario 2: A and B Revisited

Initially, A began a business with Rs 4500, and B joined after with Rs 5400. The profits at the end of the year are divided in the ratio 2:1. We have to determine when B joined.

Let M denote the number of months after which B joined. The relationship can be expressed as:

Rs 4500 * 12 : Rs 5400 * (12 - M) 2 : 1

From this, we can solve for M as follows:

12 * 4500 2 * 5400 * (12 - M)

Simplifying this, we find:

M 7 months

Scenario 3: Mohan and Sohan

Mohan invested Rs. 1 lac in a garment business for 360 days, and it returns a profit of Rs. 10 every 30 days. Sohan joined after X days with an investment of Rs. 60000. Their profits at the end of 360 days are in the ratio 3:1.

Let's break it down:

Total profit for Mohan 10 * (360 / 30) 120000

Let Sohan's profit be P. Thus:

120000 / P 3 / 1

P 40000

Using the profit formula for Sohan:

60000 / 30 * X 40000

X 200 days

This means Sohan joined 200 days after Mohan started the business, i.e., 5 months and 10 days later.

These scenarios illustrate the principle that the duration of investment and the timing of joining significantly affect the proportional sharing of profits. Understanding these dynamics can help in making informed decisions about when and how much to invest in a business venture.

Conclusion

By examining these cases, we can see how the principles of proportional investment and varying joining periods impact profit sharing in a business partnership. Calculating the exact timing and proportion of investments is essential to ensure fair returns and strategic planning for future ventures.