Mr Smith sold shares of an Indian company of rupees 25 giving 8% dividend at rupees 10 and invested the earning in rupees 15 shares paying 10% dividend at 40% premium. If the charge in his annual income is 243 rupees find the number of shares sold by Mr Smith.

Let's break down the problem to solve for the number of shares sold by Mr. Smith.

### Step 1: Understanding the original situation

1. **Original shares**:
   - Face value of the shares: ₹25 each
   - Dividend rate: 8%
   - Selling price: ₹10 per share

   The dividend earned per share is:

   \[
   \text{Dividend per share} = 8\% \times 25 = \frac{8}{100} \times 25 = 2 \, \text{rupees per share}.
   \]

### Step 2: Understanding the new investment

2. **New shares**:
   - Face value of the new shares: ₹15 each
   - Dividend rate: 10%
   - Buying price: 40% premium on face value
   
   The price at which Mr. Smith buys the new shares is:

   \[
   \text{Buying price} = 15 + 40\% \times 15 = 15 + \frac{40}{100} \times 15 = 15 + 6 = 21 \, \text{rupees}.
   \]

   The dividend earned per share for the new investment is:

   \[
   \text{Dividend per new share} = 10\% \times 15 = \frac{10}{100} \times 15 = 1.5 \, \text{rupees per share}.
   \]

### Step 3: Let the number of shares sold be \(x\)

- Total dividend from the original shares: \(2x \, \text{rupees}\)
- Mr. Smith sells these shares at ₹10 per share, so the total money he gets from selling \(x\) shares is:

  \[
  \text{Total money from selling} = 10x \, \text{rupees}.
  \]

- With this amount, he invests in the new shares priced at ₹21 each, so the number of new shares he can buy is:

  \[
  \text{Number of new shares} = \frac{10x}{21}.
  \]

- The total dividend from the new shares is:

  \[
  \text{Total dividend from new shares} = 1.5 \times \frac{10x}{21} = \frac{15x}{21} = \frac{5x}{7}.
  \]

### Step 4: Change in annual income

The change in annual income is given as 243 rupees. Therefore, the difference in the dividend between the original shares and the new shares is:

\[
2x - \frac{5x}{7} = 243.
\]

### Step 5: Solving the equation

\[
2x - \frac{5x}{7} = 243
\]

Multiply through by 7 to eliminate the fraction:

\[
14x - 5x = 1701
\]

\[
9x = 1701
\]

\[
x = \frac{1701}{9} = 189.
\]

### Conclusion:

The number of shares sold by Mr. Smith is **189**.

---

Would you like more details on any step or have further questions? Here are 5 related questions for further exploration:

1. How does the dividend rate affect the overall income from shares?
2. What is the importance of premium when buying shares?
3. How would the result change if the dividend on the new shares was higher?
4. What would happen if the selling price of the old shares was higher than ₹10?
5. How do different investment strategies impact long-term returns?

**Tip:** Always calculate both the dividend income and the buying price carefully to assess the impact on your investments.

Mr Smith sold shares of an Indian company of rupees 25 giving 8% dividend at rupees 10 and invested the earnings in rupees 15 shares paying 10% dividend at 40% premium. If the change in his annual income is 243 rupees, find the number of shares sold by Mr. Smith.

Learn how to calculate the number of shares sold by Mr. Smith, given an 8% dividend on shares with a 40% premium on new investments. This problem involves algebra, dividend calculations, and premium pricing, suitable for Grades 10-12.

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