Q 2 - If an amount of Rs. 20000 and Rs. 25000 invested by two partners in a business. But B left the business hand C joined the business with the capital of Rs. 15000 after the period of 4 year. An amount of Rs. 46000 earned as profit by the firm then what should be the share in profit of C?

To determine the share of profit for partner C, we need to consider the time and capital each partner contributed to the business.

### Step 1: Determine the capitals invested and the periods
- Partner A invested Rs. 20,000 for the entire period of 4 years.
- Partner B invested Rs. 25,000 for 4 years, but left the business after 4 years.
- Partner C joined after 4 years with Rs. 15,000 and stayed for 4 years (since the total period is 4 years, C was present only in the last year).

### Step 2: Calculate the total profit-sharing ratio
The profit-sharing ratio is calculated based on the product of capital and the time for which it was invested.

- **A's contribution**: \( 20,000 \times 4 = 80,000 \)
- **B's contribution**: \( 25,000 \times 4 = 100,000 \)
- **C's contribution**: \( 15,000 \times 1 = 15,000 \)

So, the profit-sharing ratio is:

\[
\text{A : B : C} = 80,000 : 100,000 : 15,000
\]

Simplifying the ratio by dividing by 5,000:

\[
\text{A : B : C} = 16 : 20 : 3
\]

### Step 3: Calculate C's share of the profit
Total profit = Rs. 46,000.

The total parts of the ratio = \( 16 + 20 + 3 = 39 \) parts.

C's share of profit:

\[
\text{C's share} = \frac{3}{39} \times 46,000 = \frac{3 \times 46,000}{39} = \frac{138,000}{39} \approx 3538.46 \text{ Rs.}
\]

### Answer:
Partner C's share of the profit is approximately **Rs. 3,538.46**.

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Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would the profit share change if C had invested Rs. 20,000 instead of Rs. 15,000?
2. What would happen to C's share if the total profit was Rs. 50,000?
3. How would the profit-sharing ratio change if B had stayed in the business longer?
4. What would C's share be if they had joined after 2 years instead of 4?
5. How is the profit divided if all three partners had invested different amounts at different times?

**Tip:** In business partnership problems, always account for both the amount of investment and the duration of the investment when calculating profit shares.

Q 2 - If an amount of Rs. 20000 and Rs. 25000 invested by two partners in a business. But B left the business and C joined the business with the capital of Rs. 15000 after the period of 4 years. An amount of Rs. 46000 earned as profit by the firm then what should be the share in profit of C?

Determine the share of profit for partner C in a business partnership where partners invested varying amounts over different periods. Learn how to use profit-sharing ratios and calculate individual profit shares. Suitable for students in Grades 9-11.

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