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The question you’ve shared is about Aman holding shares and conducting transactions based on a rise in share prices. Let’s break it down and calculate step-by-step:

### Given:
- Aman has **500 shares** initially, each quoted at **₹100**.
- Dividend rate is **10%** on these shares.
- When the share price rises to **₹200**, Aman sells **all his shares**.
- He invests half of the sale proceeds in **₹10, 12% shares at ₹25 each**.
- The remaining proceeds are invested in **₹400, 9% shares at ₹500 each**.

We need to find:
1. **(a) Sales proceeds**.
2. **(b) Investment in ₹10, 12% shares at ₹25**.
3. **(c) Original income**.
4. **(d) Change in income**.

### Steps:
#### 1. Sales Proceeds:
- Aman initially holds **500 shares at ₹100**. 
- When the price rises to **₹200**, he sells all the shares.
- **Sales proceeds = 500 shares × ₹200 = ₹100,000.**

#### 2. Investment in ₹10, 12% shares at ₹25:
- Half of the sales proceeds are invested in **₹10, 12% shares at ₹25 each**.
- Half of ₹100,000 = **₹50,000**.
- The price of one share = ₹25.
- Number of ₹10 shares bought = \( \frac{₹50,000}{₹25} = 2000 \) shares.

#### 3. Original Income:
- Aman initially had **500 shares at ₹100 each**, with a **10% dividend**.
- Dividend = 10% of ₹100 = ₹10 per share.
- **Total original income = 500 shares × ₹10 = ₹5,000.**

#### 4. Change in Income:
- From the ₹10, 12% shares:
    - Dividend per share = 12% of ₹10 = ₹1.20 per share.
    - Income from 2000 shares = 2000 × ₹1.20 = **₹2,400**.
- From the remaining ₹50,000:
    - Investment in ₹400, 9% shares at ₹500 = ₹50,000 ÷ ₹500 = 100 shares.
    - Dividend per share = 9% of ₹400 = ₹36 per share.
    - Income from 100 shares = 100 × ₹36 = **₹3,600**.
- **Total new income** = ₹2,400 + ₹3,600 = ₹6,000.

#### Change in Income:
- Original income = ₹5,000.
- New income = ₹6,000.
- **Change in income = ₹6,000 - ₹5,000 = ₹1,000**.

### Summary of Answers:
- **(a)** Sales proceeds: **₹100,000**.
- **(b)** Investment in ₹10, 12% shares at ₹25: **2000 shares**.
- **(c)** Original income: **₹5,000**.
- **(d)** Change in income: **₹1,000**.

Would you like further details on any part of the solution or have any other questions?

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Here are some related questions for further practice:
1. What would be Aman’s total income if he had not reinvested the sale proceeds?
2. How would the income change if the ₹400 shares gave a 10% dividend instead of 9%?
3. What if Aman only sold 50% of his shares when the price rose to ₹200?
4. How would the outcome change if the ₹10 shares were bought at ₹30 instead of ₹25?
5. What would be the impact on income if the dividend rate for ₹10 shares dropped to 8%?

**Tip:** When dealing with dividend-related problems, always start by computing the income from dividends separately before any price changes.

Aman has 500 shares each quoted at ₹100. When the share price rises to ₹200, he sells all his shares. Aman then invests half of the sale proceeds in ₹10, 12% shares at ₹25 each and the remaining in ₹400, 9% shares at ₹500 each. Find the sales proceeds, the investment in ₹10, 12% shares, the original income, and the change in income.

Explore how to calculate sales proceeds, investment in shares, and changes in income with Aman's example. This scenario uses arithmetic operations, percentage calculations, and investment analysis to understand the financial outcomes of selling and investing in shares. Suitable for students in Grades 10-12.

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