A man invests `1680rs` in buying shares of nominal value `24rs` and selling at `12%` premium. The dividend on the shares is `15%` per annum . Calculate
(i) the number of shares he buys,
(ii) the dividend he receives annually

Answer

To solve the problem step by step, we will follow the outlined procedure:

### Step 1: Determine the Nominal Value of One Share
The nominal value of one share is given as:
\[ \text{Nominal Value} = 24 \text{ Rs} \]

### Step 2: Calculate the Market Value of One Share
The market value of one share is calculated by adding the premium to the nominal value. The premium is 12% of the nominal value.
\[ \text{Premium} = 12\% \text{ of } 24 = \frac{12}{100} \times 24 = 2.88 \text{ Rs} \]
Thus, the market value of one share is:
\[ \text{Market Value} = \text{Nominal Value} + \text{Premium} = 24 + 2.88 = 26.88 \text{ Rs} \]

### Step 3: Calculate the Number of Shares Purchased
The number of shares purchased can be calculated using the formula:
\[ \text{Number of Shares} = \frac{\text{Total Investment}}{\text{Market Value of One Share}} \]
Substituting the values:
\[ \text{Number of Shares} = \frac{1680}{26.88} \approx 62.5 \]
Since shares cannot be in fractions, this indicates that the man can purchase 62 shares.

### Step 4: Calculate the Total Nominal Value of Shares Purchased
The total nominal value of the shares purchased is:
\[ \text{Total Nominal Value} = \text{Number of Shares} \times \text{Nominal Value of One Share} = 62 \times 24 = 1488 \text{ Rs} \]

### Step 5: Calculate the Annual Dividend Received
The annual dividend is calculated using the formula:
\[ \text{Dividend} = \text{Dividend Percentage} \times \text{Total Nominal Value} \]
Substituting the values:
\[ \text{Dividend} = 15\% \text{ of } 1488 = \frac{15}{100} \times 1488 = 223.2 \text{ Rs} \]

### Final Answers
(i) The number of shares he buys is approximately **62 shares**.
(ii) The dividend he receives annually is approximately **223.2 Rs**.

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