A man buys `50rs` shares of a company, paying 12 percent dividend at a premium of `10rs` Find :
(i) the market value of 320 shares
(ii) his annual income
(iii) his profit percent

Answer

Let's solve the problem step by step.

### Given:
- Nominal value of each share = ₹50
- Dividend = 12%
- Premium = ₹10
- Number of shares = 320

### Step 1: Calculate the Market Value of One Share
The market value of one share can be calculated as follows:
\[ \text{Market Value} = \text{Nominal Value} + \text{Premium} \]
\[ \text{Market Value} = 50 + 10 = ₹60 \]

### Step 2: Calculate the Market Value of 320 Shares
To find the market value of 320 shares, we multiply the market value of one share by the number of shares:
\[ \text{Market Value of 320 Shares} = \text{Market Value of One Share} \times \text{Number of Shares} \]
\[ \text{Market Value of 320 Shares} = 60 \times 320 = ₹19,200 \]

### Step 3: Calculate the Nominal Value of 320 Shares
The nominal value of 320 shares can be calculated as follows:
\[ \text{Nominal Value of 320 Shares} = \text{Nominal Value of One Share} \times \text{Number of Shares} \]
\[ \text{Nominal Value of 320 Shares} = 50 \times 320 = ₹16,000 \]

### Step 4: Calculate the Annual Income
The annual income can be calculated using the formula for dividend:
\[ \text{Annual Income} = \left(\frac{\text{Dividend}}{100}\right) \times \text{Nominal Value of 320 Shares} \]
\[ \text{Annual Income} = \left(\frac{12}{100}\right) \times 16,000 = ₹1,920 \]

### Step 5: Calculate the Profit Percent
To find the profit percent, we first need to determine the profit. The profit is the annual income earned from the shares minus the total investment:
\[ \text{Profit} = \text{Annual Income} - \text{Market Value of 320 Shares} \]
Since the man invested ₹19,200 and earned ₹1,920 as annual income, the profit percent can be calculated as:
\[ \text{Profit Percent} = \left(\frac{\text{Annual Income}}{\text{Market Value of 320 Shares}}\right) \times 100 \]
\[ \text{Profit Percent} = \left(\frac{1,920}{19,200}\right) \times 100 = 10\% \]

### Final Answers:
(i) Market value of 320 shares = ₹19,200
(ii) Annual income = ₹1,920
(iii) Profit percent = 10%

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