Which of the following statement(s) is/are necessary to determine the total profit earned in the business at the end of the year?

**Statement 1:** A and B entered into a partnership by investing Rs. $(X+1000)$ and Rs. $(Y+1000)$ respectively. C joined them after 3 months with an investment of Rs. $Z$.

**Statement 2:** At the end of the year, C's share of the profit is Rs. $12000$.

**Statement 3:** The difference between the profit shares of A and B after one year is Rs. $1500$.

Question

Which of the following statement(s) is/are necessary to determine the total profit earned in the business at the end of the year?

**Statement 1:** A and B entered into a partnership by investing Rs. $(X+1000)$ and Rs. $(Y+1000)$ respectively. C joined them after 3 months with an investment of Rs. $Z$.

**Statement 2:** At the end of the year, C's share of the profit is Rs. $12000$.

**Statement 3:** The difference between the profit shares of A and B after one year is Rs. $1500$.

Accepted Answer

**Solution:**

1. To find the total profit earned, we need to understand the investment and time period of each partner to calculate their profit shares.

2. **Statement 1** gives the initial investments of A and B and mentions that C joined after 3 months with investment Rs. $Z$. This is crucial to determine the ratio of investments considering the time period.

3. **Statement 2** provides C's profit share at the end of the year, which helps relate the total profit to C's share.

4. **Statement 3** gives the difference between the profit shares of A and B, which is necessary to find the exact ratio between A and B's investments or profits.

5. Using all three statements together, we can set up equations based on the profit sharing formula:

- Profit share is proportional to investment × time.
   - From Statement 1, we know investments and time periods.
   - From Statement 2 and 3, we get values related to profit shares.

6. These equations allow us to solve for the total profit.

**Answer:** All together

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