A man invests a certain sum in buying `15%` `100rs` shares at `20%` premium. Find :
(i) his income from one share.
(ii) the number of shares bought to have an income, from the dividend `6480rs`
(iii) sum invested

Answer

Let's solve the problem step by step.

### Given:
- Dividend rate = 15%
- Face value of shares = ₹100
- Premium = 20%

### Step 1: Find the income from one share.
The income from one share can be calculated using the formula:
\[ \text{Income from one share} = \text{Dividend} = \left(\frac{\text{Dividend rate}}{100} \times \text{Face value}\right) \]
Substituting the values:
\[ \text{Income from one share} = \left(\frac{15}{100} \times 100\right) = 15 \text{ rupees} \]

### Step 2: Find the number of shares bought to have an income of ₹6480.
To find the number of shares, we use the formula:
\[ \text{Number of shares} = \frac{\text{Total income}}{\text{Income from one share}} \]
Substituting the values:
\[ \text{Number of shares} = \frac{6480}{15} = 432 \]

### Step 3: Find the total sum invested.
To find the total sum invested, we first need to calculate the market value of one share. The market value can be calculated as:
\[ \text{Market value} = \text{Face value} + \text{Premium} = 100 + \left(\frac{20}{100} \times 100\right) = 100 + 20 = 120 \text{ rupees} \]
Now, we can calculate the total investment:
\[ \text{Total investment} = \text{Number of shares} \times \text{Market value} \]
Substituting the values:
\[ \text{Total investment} = 432 \times 120 = 51840 \text{ rupees} \]

### Summary of Answers:
(i) Income from one share = ₹15
(ii) Number of shares bought = 432
(iii) Total sum invested = ₹51,840

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