Understanding Partnership Profit Sharing

In a business partnership, the profit or loss is typically shared among the partners in the ratio of their effective capital investment and the duration for which the capital was invested. When the investments change over time, we calculate the equivalent investment for the entire duration, often expressed as 'investment-months' or 'investment-time units'.

Here's how we calculate the share of each partner based on their varying investments over the year:

The total duration of the partnership is 1 year, which is 12 months.

Partner A's Investment:

• Initial investment: Rs. 29,000 for the first 4 months.
• After 4 months, A withdrew Rs. 3,000.
• New investment: $29,000 - 3,000 = \text{Rs. } 26,000$ for the remaining $12 - 4 = 8$ months.
• A's total investment-months: $(29,000 \times 4) + (26,000 \times 8)$
• A's total investment-months: $116,000 + 208,000 = 324,000$

Partner B's Investment:

• Initial investment: Rs. 25,000 for the entire year (12 months).
• B's total investment-months: $(25,000 \times 12)$
• B's total investment-months: $300,000$

Partner C's Investment:

• Initial investment: Rs. 25,000 for the first $4 + 2 = 6$ months. (Initially 4 months, then 2 more months passed before C changed investment)
• After $4 + 2 = 6$ months, C invested Rs. 12,000 more.
• New investment: $25,000 + 12,000 = \text{Rs. } 37,000$ for the remaining $12 - 6 = 6$ months.
• C's total investment-months: $(25,000 \times 6) + (37,000 \times 6)$
• C's total investment-months: $150,000 + 222,000 = 372,000$

Ratio of Investment-Months:

The ratio of investment-months for A, B, and C is:

$A : B : C = 324,000 : 300,000 : 372,000$

We can simplify this ratio by dividing each number by 1,000:

$324 : 300 : 372$

Further simplifying by dividing each number by their greatest common divisor, which is 12:

$324 \div 12 = 27$

$300 \div 12 = 25$

$372 \div 12 = 31$

The simplified ratio of profit sharing among A, B, and C is $27 : 25 : 31$.

Calculating Shares in Total Profit:

The total profit at the end of the year is Rs. 33,200.

The sum of the ratio parts is $27 + 25 + 31 = 83$.

To find the share of each partner, we divide the total profit by the sum of the ratio parts and then multiply by the individual ratio part.

A's share $= \frac{27}{83} \times 33,200$

B's share $= \frac{25}{83} \times 33,200$

C's share $= \frac{31}{83} \times 33,200$

We need to find the share of C. Let's calculate C's share:

C's share $= \frac{31}{83} \times 33,200$

First, calculate $\frac{33,200}{83}$:

$\frac{33,200}{83} = 400$

Now, multiply this by C's ratio part:

C's share $= 31 \times 400 = 12,400$

So, C's share in the profit of Rs. 33,200 is Rs. 12,400.

The ratio of shares A:B:C is $324,000 : 300,000 : 372,000$, which simplifies to $27 : 25 : 31$. The total ratio parts are 83. C's share is $\frac{31}{83}$ of the total profit.

C's share in profit $= \frac{31}{83} \times 33,200 = 12,400$.

Revision Table: Partnership Profit Calculation

Additional Information: Partnership Basics

A partnership is a business structure where two or more individuals agree to share in the profits or losses of a business. Key aspects include:

• Partnership Deed: A legal agreement outlining terms like profit/loss sharing ratio, capital contributions, roles, responsibilities, interest on capital, drawings, etc. If no deed exists, the law usually stipulates equal profit sharing and no interest on capital/drawings.
• Capital Contribution: The initial funds or assets contributed by each partner to start the business.
• Profit and Loss Sharing Ratio: The proportion in which partners divide the business's net profit or loss. This is usually based on the partnership deed. If investments vary over time, the ratio is calculated based on the time-weighted average investment, as shown in this problem using investment-months.
• Types of Partners: Can include active partners (involved in day-to-day management) and sleeping/dormant partners (invest capital but not involved in management).

Understanding how profit is distributed based on investment and time is crucial for partnership accounts and business calculations.