Salman invests a sum of money in `50rs` shares paying `15%` dividend quoted at `20%` premium. If his annual dividend is `600rs`, calculate
(i) the number of shares he bought
(ii) his total investment
(iii) the rate of return on his investment

Answer

Let's solve the problem step by step.

### Given:
- Nominal value of each share (N) = ₹50
- Dividend percentage = 15%
- Premium = 20%
- Annual dividend = ₹600

### Step 1: Calculate the Market Value of Each Share
The market value of each share is calculated as follows:
\[ \text{Market Value} = \text{Nominal Value} + \text{Premium} \]
\[ \text{Premium} = 20\% \text{ of } 50 = \frac{20}{100} \times 50 = ₹10 \]
\[ \text{Market Value} = 50 + 10 = ₹60 \]

### Step 2: Calculate the Number of Shares Bought
We know that the annual dividend can be expressed as:
\[ \text{Annual Dividend} = \text{Number of Shares} \times \text{Dividend per Share} \]
Where the dividend per share is calculated as:
\[ \text{Dividend per Share} = \frac{\text{Dividend Percentage}}{100} \times \text{Nominal Value} = \frac{15}{100} \times 50 = ₹7.5 \]
Let the number of shares be \( n \). Thus, we have:
\[ 600 = n \times 7.5 \]
Solving for \( n \):
\[ n = \frac{600}{7.5} = 80 \]

### Step 3: Calculate Total Investment
Total investment can be calculated as:
\[ \text{Total Investment} = \text{Number of Shares} \times \text{Market Value} \]
Substituting the values:
\[ \text{Total Investment} = 80 \times 60 = ₹4800 \]

### Step 4: Calculate the Rate of Return on Investment
The rate of return can be calculated using the formula:
\[ \text{Rate of Return} = \left( \frac{\text{Dividend}}{\text{Total Investment}} \right) \times 100 \]
Substituting the values:
\[ \text{Rate of Return} = \left( \frac{600}{4800} \right) \times 100 = 12.5\% \]

### Summary of Results
(i) Number of shares bought = 80
(ii) Total investment = ₹4800
(iii) Rate of return on investment = 12.5%