A company declares a dividend of `11.2%` to all its share holders. If its `60rs` share is available in the market at a premium of `25%`, how much should Rakesh invest, in buying the shares of this company, in order to have an annual income of `1680rs` ?

Answer

To solve the problem step by step, we will follow the given information and calculations:

### Step 1: Determine the Market Value of One Share
The nominal (face) value of one share is given as `60 Rs`. The share is available at a premium of `25%`.

**Calculation:**
- Premium = 25% of 60 Rs = \( \frac{25}{100} \times 60 = 15 \) Rs
- Market Value = Nominal Value + Premium = \( 60 + 15 = 75 \) Rs

### Step 2: Understand the Dividend
The company declares a dividend of `11.2%`. This means that the dividend is calculated on the nominal value of the shares.

### Step 3: Set Up the Equation for Annual Income
Rakesh wants an annual income of `1680 Rs` from the dividends. Let’s denote the number of shares Rakesh buys as `N`.

The dividend earned from `N` shares can be expressed as:
- Dividend = Dividend Percentage × Nominal Value × Number of Shares
- \( 1680 = 11.2\% \times 60 \times N \)

### Step 4: Solve for the Number of Shares (N)
Convert the percentage to a decimal for calculation:
- \( 11.2\% = \frac{11.2}{100} = 0.112 \)

Now substitute this into the equation:
- \( 1680 = 0.112 \times 60 \times N \)

**Calculation:**
- \( 1680 = 6.72 \times N \)
- \( N = \frac{1680}{6.72} \)
- \( N = 250 \)

### Step 5: Calculate the Total Investment
Now that we know Rakesh needs to buy `250` shares, we can calculate the total investment required.

**Calculation:**
- Total Investment = Number of Shares × Market Value per Share
- Total Investment = \( 250 \times 75 \)
- Total Investment = \( 18750 \) Rs

### Conclusion
Rakesh should invest **18750 Rs** to achieve an annual income of **1680 Rs** from the dividends.

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