Calculating Profit Shares in a Partnership: A Comprehensive Tutorial

Understanding the intricacies of profit sharing in a partnership, especially when there are changes in capital contributions due to withdrawals and reinvestments, is crucial for accurate financial management. In this article, we will walk through a detailed example to illustrate the step-by-step process of calculating X’s share of the profit. Let's break down the problem and work through it systematically.

Problem Statement

X and Y entered into partnership with investments of 700 and 600 respectively. After 3 months, X withdrew 2/7 of his stock but after 3 months he reinvested 3/5 of the withdrawn amount. The profit at the end of the year is 726. How much of this should X receive?

Step-by-Step Solution

Step 1: Calculate the Capital Contributions

Initial Investments

X's Contribution Over Time

For the first 3 months, X's capital is 700.

After 3 months, X withdraws 2/7 of his capital:

Withdrawal: (frac{2}{7} times 700 200)

So after 3 months, X's remaining capital is:

Remaining Capital: 700 - 200 500

After another 3 months (total of 6 months), X reinvests 3/5 of the withdrawn amount:

Reinvestment: (frac{3}{5} times 200 120)

Therefore, after 6 months, X's capital becomes:

Total Capital Post-Reinvestment: 500 120 620

From months 6 to 12, X's capital is 620.

Total Capital Contributions

From months 0 to 3, X's capital is 700.

From months 3 to 6, X's capital is 500.

From months 6 to 12, X's capital is 620.

The total capital contribution for X is calculated as follows:

X's Total Contribution: (700 times 3 500 times 3 620 times 6 2100 1500 3720 7320)

Y's Contribution Over Time

Y's capital remains constant at 600 for the entire year.

Therefore, Y's total contribution is:

Y's Total Contribution: (600 times 12 7200)

Step 2: Calculate the Profit Share

Total Contributions

The total contributions are:

Total Contribution: 7320 7200 14520

X's and Y's Shares of the Total Contribution

X's Share: (frac{7320}{14520})

Y's Share: (frac{7200}{14520})

Step 3: Calculate X's Profit

The total profit at the end of the year is 726. To find X's share of the profit:

X's Profit: (726 times frac{7320}{14520})

Calculating this:

X's Profit: (726 times frac{7320}{14520} approx 364.00)

Conclusion

Thus, the amount X should receive from the profit is approximately $364.00.