How much should a man invest in `80rs` shares selling at `75rs` to obtain an annual income of `1080rs` , if the dividend declared is 15 percent ?

Answer

To solve the problem step by step, we need to determine how much a man should invest in shares to achieve an annual income of ₹1080, given that the shares have a nominal value of ₹80, are selling at ₹75, and the declared dividend is 15%.

### Step 1: Understand the given values
- Nominal value of one share (Face value) = ₹80
- Market value of one share = ₹75
- Annual income desired = ₹1080
- Dividend declared = 15%

### Step 2: Set up the equation for dividend
The formula for dividend is given by:
\[ \text{Dividend} = \text{Number of Shares} \times \text{Nominal Value of Share} \times \frac{\text{Dividend Percentage}}{100} \]
Let the number of shares be \( n \).

### Step 3: Substitute the known values into the equation
We know the annual income (dividend) is ₹1080. Therefore, we can write:
\[ 1080 = n \times 80 \times \frac{15}{100} \]

### Step 4: Simplify the equation
This simplifies to:
\[ 1080 = n \times 80 \times 0.15 \]
\[ 1080 = n \times 12 \]

### Step 5: Solve for \( n \)
To find \( n \), divide both sides by 12:
\[ n = \frac{1080}{12} = 90 \]

### Step 6: Calculate the total investment
Now, we need to find the total investment based on the market value of the shares:
\[ \text{Total Investment} = \text{Number of Shares} \times \text{Market Value of One Share} \]
Substituting the values:
\[ \text{Total Investment} = 90 \times 75 = 6750 \]

### Final Answer
The man should invest ₹6750 to obtain an annual income of ₹1080 from the shares.

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