Understanding Profit Sharing in Business Partnerships

In a business partnership, profits are typically shared among partners based on their investment and the duration for which their investment remained in the business. The basic principle is that the profit share of a partner is proportional to the product of their invested capital and the time period for which the capital was invested.

Let's analyze the investments made by A, B, and C in this business:

• A's Investment: Rs. 20000 for 1 year.
• B's Investment: Rs. 30000 for 2 years.
• C's Investment: Rs. 40000 for 2 years.

To find the ratio in which the profit will be shared, we calculate the 'equivalent investment units' for each partner by multiplying the amount invested by the time period (in years).

Calculating Equivalent Investment Units

• Equivalent investment unit for A = Amount invested by A × Time for which A invested
• Equivalent investment unit for B = Amount invested by B × Time for which B invested
• Equivalent investment unit for C = Amount invested by C × Time for which C invested

Let's calculate these values:

• A's equivalent investment unit = $\text{Rs. } 20000 \times 1 \text{ year} = 20000$
• B's equivalent investment unit = $\text{Rs. } 30000 \times 2 \text{ years} = 60000$
• C's equivalent investment unit = $\text{Rs. } 40000 \times 2 \text{ years} = 80000$

Determining the Profit Sharing Ratio

The ratio of the profit shares of A, B, and C will be the ratio of their equivalent investment units.

Ratio A : B : C = A's equivalent unit : B's equivalent unit : C's equivalent unit

Ratio A : B : C = $20000 : 60000 : 80000$

We can simplify this ratio by dividing each number by the greatest common divisor, which is 20000.

Ratio A : B : C = $\frac{20000}{20000} : \frac{60000}{20000} : \frac{80000}{20000}$

Ratio A : B : C = $1 : 3 : 4$

This ratio $1:3:4$ represents how the total profit of Rs. 32000 will be divided among A, B, and C.

Calculating A's Share of the Profit

The total number of ratio parts is the sum of the individual parts: $1 + 3 + 4 = 8$.

A's share of the profit is A's ratio part divided by the total ratio parts, multiplied by the total profit.

A's share = $\left( \frac{\text{A's ratio part}}{\text{Total ratio parts}} \right) \times \text{Total Profit}$

A's share = $\left( \frac{1}{8} \right) \times \text{Rs. } 32000$

A's share = $\frac{32000}{8}$

A's share = $\text{Rs. } 4000$

Therefore, A's share in the net profit of Rs. 32000 is Rs. 4000.

To verify, we could also calculate B's and C's shares:

• B's share = $\left( \frac{3}{8} \right) \times \text{Rs. } 32000 = 3 \times 4000 = \text{Rs. } 12000$
• C's share = $\left( \frac{4}{8} \right) \times \text{Rs. } 32000 = 4 \times 4000 = \text{Rs. } 16000$

Total profit = A's share + B's share + C's share = $4000 + 12000 + 16000 = 32000$. This matches the given total profit.