https://file.aiquickdraw.com/mathbot/file/1725391480412i4a5ivww.jpg

Thank you for uploading the image. The image contains multiple-choice questions related to investments, profit-sharing, and percentages involving companies A, B, C, and D. Let's solve the questions one by one.

### Question XXI:
**Companies A, B, and C started a business P by investing Rs. 4200 each. After 1 year of business P:**

1. The companies added some amount to their initial investments.
2. Company A invested 26.96% more than its initial investment.
3. Company B invested 14.28% more than its initial investment.
4. Company C invested 62.84% more than its initial investment.

Company D is involved later, with Company P for 3 years. A, B, C, and D are in the profit ratio of 5:4:7:3.

**Find D’s investment if Company P's total profit is distributed among A, B, C, and D in the given ratio.**

Given the above, let's analyze the individual investments:

- Initial investment by A, B, and C = Rs. 4200 each.

**1. Calculating new investments:**

   - **Company A's investment:**
     \[
     \text{Investment} = 4200 + 26.96\% \text{ of } 4200
     \]
     \[
     = 4200 + \left( \frac{26.96}{100} \times 4200 \right)
     \]
     \[
     = 4200 + 1132.32 = 5332.32 \, \text{Rs}
     \]

   - **Company B's investment:**
     \[
     \text{Investment} = 4200 + 14.28\% \text{ of } 4200
     \]
     \[
     = 4200 + \left( \frac{14.28}{100} \times 4200 \right)
     \]
     \[
     = 4200 + 599.76 = 4799.76 \, \text{Rs}
     \]

   - **Company C's investment:**
     \[
     \text{Investment} = 4200 + 62.84\% \text{ of } 4200
     \]
     \[
     = 4200 + \left( \frac{62.84}{100} \times 4200 \right)
     \]
     \[
     = 4200 + 2640.48 = 6840.48 \, \text{Rs}
     \]

**2. Given profit sharing ratio of A, B, C, D: 5:4:7:3**

   If we assume D invested for 3 years while others for 2 years, and the total profit ratio is given as 5:4:7:3, then:
   - Let investment by D be \( x \) Rs.
   
   To maintain the given profit ratio:
   - For Company D:
     \[
     \frac{3x}{x} = 3
     \]

Given the ratio is directly provided in terms of the profit distribution, the investment calculations align with profit directly.

### Next Steps
I will proceed with solving the remaining parts based on this calculation, focusing on other company-related problems if applicable. Let's verify any additional data or requirements as per other parts mentioned.

Would you like to continue with further details, or focus on a specific problem statement?

### Additional Related Questions
1. What would be the total profit if D’s share of profit is known?
2. How can the profit-sharing ratio be verified with the given percentage changes?
3. How does the involvement of company D affect the overall profit distribution over time?
4. How is the profit distribution affected by different investment timespans among companies?
5. What would happen if another company joined at a different investment amount?

### Tip
To handle questions involving percentage increase/decrease in investments, always convert the percentage into decimal form before calculations. This ensures accuracy in determining the increased or decreased amount.

Companies A, B, and C start a business by investing Rs. 4200 each. After the completion of 1 year of business P, the companies added some amount to their initial investments. Company A invested 26.96% more than its initial investment, Company B invested 14.28% more, and Company C invested 62.84% more. Company D joins the business for 3 years and the total profit ratio between A, B, C, and D is 5:4:7:3. Find the total profit distributed among the companies.

Learn how to calculate the total profit distributed among companies A, B, C, and D, given their investment increases and the profit-sharing ratio. This problem involves percentage increase calculations and understanding profit distribution based on ratios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation