Partner Profit Sharing in a Business Partnership

In a business partnership, the way profits are shared among partners often depends on their respective investments and the time period for which they have invested. This article explores a scenario where three partners, A, B, and C, invest different amounts for varying periods and how to calculate the share of profit for each partner.

Investment and Time Periods

Let's consider a partnership where Partner A invests 1/6th of the capital for 1/6 of the time, Partner B invests 1/3 of the capital for 1/3 of the time, and Partner C invests the remaining capital for the entire year. At the end of the year, the profit earned is Rs 23000.

Effective Capital Contribution

The formula for calculating the effective capital contribution is as follows:

Partner A

Investment: 1/6th of the capital Time: 1/6 of the year Effective Contribution: (1/6) × (1/6) 1/36

Partner B

Investment: 1/3 of the capital Time: 1/3 of the year Effective Contribution: (1/3) × (1/3) 1/9

Partner C

Investment: Remaining capital 1 - (1/6 1/3) 1 - (1/6 2/6) 1 - 3/6 1/2 Time: Entire year (1 year) Effective Contribution: (1/2) × 1 1/2

Total Effective Contributions

Now, we sum the effective contributions of all partners to find the total effective contribution.

Calculation:

Total Effective Contribution (1/36) (1/9) (1/2)

To add these fractions, we need a common denominator. The least common multiple of 36, 9, and 2 is 36.

Convert (1/9) to a fraction with a denominator of 36:

(1/9) (4/36)

Convert (1/2) to a fraction with a denominator of 36:

(1/2) (18/36)

Now, we can add them:

Total Effective Contribution (1/36) (4/36) (18/36) 23/36

Share of Partner B

To find B's share of the total profit, we calculate the ratio of B's effective contribution to the total effective contribution:

B's Share (B's Effective Contribution / Total Effective Contribution) × Total Profit

B's Share ((1/9) / (23/36)) × 23000

Simplify (1/9) ÷ (23/36):

(1/9) × (36/23) 4/23

Now, calculate B's share:

B's Share (4/23) × 23000 92000/23 ≈ 4000

Conclusion

Therefore, Partner B's share of the profit is approximately Rs. 4000.

Additionally, the ratio of the shares of A, B, and C can be determined as:

Ratios

A:B:C (1/36):(1/9):(1/2) 1:4:18

Based on the ratios, if we distribute the profit of Rs. 23000, B's share would be:

B's Share (4/23) × 4600 Rs. 800