Calculating Investments in a Business Partnership

Verifying the amount invested in a business partnership requires a thorough understanding of the time and amount each partner contributes. This article will go through a detailed problem where P and Q start a business with an investment ratio and are later joined by R. We will explore the calculations to determine the amount invested by R and its significance in the business.

Initial Investment Scenario and Introduction of Partner R

P and Q started a business investing in the ratio of 5:6. After six months, R joins the business with an investment equal to Q’s initial investment. The goal is to determine the amount invested by R and the profit-sharing ratio among P, Q, and R.

Initial Variables and Contribution Calculation

Let's assume the common ratio of P and Q's investment is x. This means:

P's investment: 5x for 12 months Q's investment: 6x for 22 months (12 months 6 months) R's investment: 6x for 6 months

The total investment for the year can be calculated as:

P's investment 5x * 12 6 Q's investment 6x * 22 132x R's investment 6x * 6 36x Total investment 6 132x 36x 228x

The profit-sharing ratio among P, Q, and R can be determined by the ratio of their investments.

Profit-Sharing Calculation and Verification

The total profit earned in a year is Rs. 98000, which is 20% of the total investment. We can calculate the total investment using the profit:

Total profit (20%) 98000

Total investment 98000 / 0.2 490000

Using this total investment, we can find the individual investments:

P's investment: 6 / 228x * 490000 140000 Q's investment: 132x / 228x * 490000 264000 R's investment: 36x / 228x * 490000 60000

Since Q's investment is 264000, we can find x:

6x 264000 / 22 140000

x 140000 / 6 23333.33

Therefore, R's investment is 36x 36 * 23333.33 840000 / 6 140000

Conclusion

The amount invested by R is 140000, which is derived by considering the profit-sharing ratio and the total investment. This problem highlights the importance of understanding investment ratios and profit-sharing mechanisms in business partnerships.

Additional Considerations

Various factors can influence the investment and profit-sharing in a business. These include the duration of investment, the level of contribution, and the overall performance of the business. Understanding these factors helps in better planning and decision-making.