Understanding Partnership Profit Sharing

In a business partnership, profits are typically shared among partners based on the ratio of their capital investments and the duration for which their capital remained in the business. The total contribution of each partner to the profit is calculated by multiplying their investment amount by the time period (in months, years, etc.) for which the investment was active in the business.

Calculating Investment × Time for Each Partner

Let's analyze the investment and the duration for each partner, A, B, and C, over the period of one year (12 months):

• Partner A: Invested Rs. 100000 for the full year (12 months).
• Partner B: Invested Rs. 140000. C left after 3 months. B left 7 months after C left, which means B left after $3 + 7 = 10$ months from the start of the business.
• Partner C: Invested Rs. 200000 and left after 3 months.

Now, we calculate the product of investment and time for each partner:

• A's contribution = Investment × Time = $\text{Rs. } 100000 \times 12 \text{ months} = 1200000$
• B's contribution = Investment × Time = $\text{Rs. } 140000 \times 10 \text{ months} = 1400000$
• C's contribution = Investment × Time = $\text{Rs. } 200000 \times 3 \text{ months} = 600000$

Determining the Profit Sharing Ratio

The profit sharing ratio among A, B, and C is the ratio of their contributions (Investment × Time products):

\text{Ratio A : B : C} = 1200000 : 1400000 : 600000

We can simplify this ratio by dividing all values by 100000:

\text{Ratio A : B : C} = 12 : 14 : 6

Further simplifying the ratio by dividing by the common factor 2:

\text{Ratio A : B : C} = 6 : 7 : 3

The total parts in the ratio are $6 + 7 + 3 = 16$.

Calculating the Total Profit

We are given that C received a share of profit equal to Rs. 1155. From the ratio, C's share corresponds to 3 parts out of the total 16 parts. Let the total profit at the end of the year be P.

C's Share = $\left( \frac{\text{C's Ratio Part}}{\text{Total Ratio Parts}} \right) \times \text{Total Profit}

$1155 = \left( \frac{3}{16} \right) \times P$

To find the total profit P, we can rearrange the equation:

$P = 1155 \times \left( \frac{16}{3} \right)$

$P = \left( \frac{1155}{3} \right) \times 16$

$P = 385 \times 16$

$P = 6160$

So, the total profit at the end of the year was Rs. 6160.

Finding the Total Share of Profits of A and B

We need to find the combined share of profits for A and B. From the ratio 6 : 7 : 3, the combined ratio parts for A and B are $6 + 7 = 13$ parts.

Total Share of A and B = $\left( \frac{\text{A and B Combined Ratio Parts}}{\text{Total Ratio Parts}} \right) \times \text{Total Profit}

Total Share of A and B = $\left( \frac{13}{16} \right) \times 6160$

Total Share of A and B = $13 \times \left( \frac{6160}{16} \right)$

Total Share of A and B = $13 \times 385$

$13 \times 385 = 4995$

The total share of profits for A and B is Rs. 4995.

Based on the ratio 6 : 7 : 3, the total share for A and B is 13 parts, and C's share is 3 parts.

Given C's share = Rs. 1155 (3 parts)

Value of 1 part = $\frac{1155}{3} = \text{Rs. } 385$

Total share of A and B = 13 parts = $13 \times 385 = \text{Rs. } 4995$

Conclusion

The total share of profits of A and B is Rs. 4995.

Revision Table: Partnership Profit Calculation

Additional Information: Types of Business Partnerships

Understanding different types of partnerships can provide context for how profit-sharing agreements are structured:

• General Partnership: All partners share in the management and liability. Profits and losses are shared according to the partnership agreement.
• Limited Partnership (LP): Has at least one general partner (who has unlimited liability and manages the business) and at least one limited partner (whose liability is limited to their investment and who does not participate in management). Profit distribution varies based on the agreement.
• Limited Liability Partnership (LLP): Provides limited liability to all partners, similar to a corporation. Partners are not responsible for another partner's misconduct. Profit sharing is based on the partnership agreement.

The profit sharing method based on investment and time is a common approach in partnership agreements, ensuring that profit distribution reflects each partner's contribution.