Suman and Sukhbir started a business by investing 3000 and ₹2000 each. two months after that, Saif joined the business by investing 4004 months after Saves investment. Ashwini joined the business and invested some money. If after the end of the year, Ashwini got nine upon 34 of the total profit, then how much money he invested.

Let's solve the problem step by step.

### Problem Recap:
- **Suman** invests ₹3000.
- **Sukhbir** invests ₹2000.
- **Saif** joins 2 months later with an investment of ₹4000.
- **Ashwini** joins 4 months after Saif with an investment of \( x \) (which we need to find out).
- After one year, Ashwini gets \(\frac{9}{34}\) of the total profit.

### Steps to Solve:

1. **Investment Durations**:
   - **Suman**: 12 months.
   - **Sukhbir**: 12 months.
   - **Saif**: \(12 - 2 = 10\) months.
   - **Ashwini**: \(12 - 2 - 4 = 6\) months.

2. **Contribution in terms of "money-months"**:
   - **Suman**: \(3000 \times 12 = 36000\) money-months.
   - **Sukhbir**: \(2000 \times 12 = 24000\) money-months.
   - **Saif**: \(4000 \times 10 = 40000\) money-months.
   - **Ashwini**: \(x \times 6 = 6x\) money-months.

3. **Total money-months**:
   \[
   36000 + 24000 + 40000 + 6x = 100000 + 6x
   \]

4. **Ashwini's share of profit**:
   According to the problem, Ashwini's share of the profit is \(\frac{9}{34}\), so:
   \[
   \frac{6x}{100000 + 6x} = \frac{9}{34}
   \]

5. **Solve for \(x\)**:
   Cross-multiply to solve for \(x\):
   \[
   34 \times 6x = 9 \times (100000 + 6x)
   \]
   \[
   204x = 900000 + 54x
   \]
   \[
   204x - 54x = 900000
   \]
   \[
   150x = 900000
   \]
   \[
   x = \frac{900000}{150} = 6000
   \]

### Conclusion:
Ashwini invested ₹6000.

Would you like further clarification or have any more questions?

### Related Questions:
1. How would Ashwini's investment change if he had joined 2 months earlier?
2. What would happen if Saif had invested ₹5000 instead of ₹4000?
3. How would Suman's and Sukhbir's profits change if they invested for different durations?
4. Can you calculate each person's share of profit based on their investment?
5. How does the ratio of profit distribution relate to the "money-months" concept?

### Tip:
When solving word problems involving investments and profit sharing, breaking down the problem into clear steps, especially understanding the concept of "money-months," helps simplify the calculations.

Learn how to calculate Ashwini's investment in a business profit sharing problem where investments and profit distribution are discussed. This problem involves understanding investments over different durations and calculating profit shares based on ratios. Suitable for students and individuals interested in financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation