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Let's break down the problem step by step to solve the questions.

### Problem Statement:
- Aman has **500 shares** of a company, each share worth **₹100**, quoted at **₹120**, paying a **10% dividend**.
- When the price rises to **₹200** per share, Aman sells all his shares.
- He invests:
  - Half of the sale proceeds in **₹10 shares**, giving **12% dividend at ₹25** per share.
  - The remaining half of the sale proceeds in **₹400, 9% shares at ₹500** per share.

We need to find the following:
(a) Sales proceeds  
(b) Investment in ₹10 shares with 12% dividend at ₹25 per share  
(c) Original income  
(d) Change in income  

### (a) Sales Proceeds:
- Aman originally has **500 shares**.
- He sells them when the price rises to **₹200 per share**.

Total sales proceeds:
\[
500 \times 200 = ₹100,000
\]

### (b) Investment in ₹10, 12% shares at ₹25 per share:
- Half of the sale proceeds is invested in ₹10 shares with a 12% dividend at ₹25 per share.
- Half of the total sale proceeds = \(\frac{100,000}{2} = ₹50,000\).

Number of shares bought:
\[
\frac{₹50,000}{₹25 \, \text{per share}} = 2,000 \, \text{shares}.
\]

### (c) Original Income:
The original income comes from the dividend of the 500 shares he held.
- Dividend per share = 10% of ₹100 = ₹10.
- Total dividend income (original income):
\[
500 \times 10 = ₹5,000.
\]

### (d) Change in Income:
We need to calculate the new income and compare it with the original income to find the change.

#### Income from ₹10 shares with 12% dividend at ₹25:
- Dividend per share = 12% of ₹10 = ₹1.2.
- Income from 2,000 shares:
\[
2000 \times 1.2 = ₹2,400.
\]

#### Income from ₹400, 9% shares at ₹500:
- Remaining half of the proceeds is ₹50,000, invested in ₹400 shares at ₹500 per share.
- Number of shares bought:
\[
\frac{₹50,000}{₹500} = 100 \, \text{shares}.
\]
- Dividend per share = 9% of ₹400 = ₹36.
- Income from 100 shares:
\[
100 \times 36 = ₹3,600.
\]

#### Total new income:
\[
₹2,400 + ₹3,600 = ₹6,000.
\]

#### Change in income:
New income - Original income:
\[
₹6,000 - ₹5,000 = ₹1,000.
\]

### Final Answers:
- (a) Sales proceeds = **₹100,000**
- (b) Investment in ₹10 shares at ₹25 = **2,000 shares**
- (c) Original income = **₹5,000**
- (d) Change in income = **₹1,000**

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Would you like any further details or clarifications on any of these steps?

Here are five related questions you might explore:
1. What would happen if the price per share hadn't risen, and he sold at ₹120 instead?
2. How would the income change if the dividend rates for the new investments were different?
3. How many shares would he buy if he reinvested only 25% of the sales proceeds in ₹10 shares?
4. What is the significance of dividend yield in such investments?
5. How does changing the sale price per share impact the overall investment returns?

**Tip:** Always evaluate your income sources in investments based on both dividends and potential capital gains.

Aman has 500, ₹100 shares of a company quoted at ₹120, paying a 10% dividend. When the share price rises to ₹200 each, he sells all his shares. He invests half of the sale proceeds in ₹10, 12% shares at ₹25, and the remaining sale proceeds in ₹400, 9% shares at ₹500. Find the sales proceeds, investment in ₹10, 12% shares at ₹25, original income, and change in income.

Solve a problem involving the sale of shares at a higher price, investment of proceeds in new shares with different dividend percentages, and calculation of original and new income. The problem covers concepts of percentage, dividends, and investment returns. Suitable for students in Grades 10-12.

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