How much should a man invest in `100rs` shares selling at `110rs` to obtain an annual income of `1680rs`, if the dividend declared is `12%`

Answer

To solve the problem, we need to determine how much a man should invest in shares to obtain a specific annual income given the dividend percentage and the market price of the shares. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Nominal value of the share (face value) = ₹100
- Market value of the share = ₹110
- Annual income desired = ₹1680
- Dividend declared = 12%

2. **Calculate the Dividend per Share**:
The dividend per share can be calculated using the formula:
\[ \text{Dividend per share} = \left(\frac{\text{Dividend percentage}}{100}\right) \times \text{Nominal value} \]
Substituting the values:
\[ \text{Dividend per share} = \left(\frac{12}{100}\right) \times 100 = ₹12 \]

3. **Determine the Number of Shares Needed**:
To find out how many shares (N) are needed to achieve the desired annual income, we can use the formula:
\[ \text{Total Dividend} = \text{Number of Shares} \times \text{Dividend per Share} \]
Rearranging this gives:
\[ N = \frac{\text{Total Dividend}}{\text{Dividend per Share}} = \frac{1680}{12} \]
Calculating this:
\[ N = 140 \]

4. **Calculate the Total Investment**:
Now that we know the number of shares, we can calculate the total investment using the market value of the shares:
\[ \text{Total Investment} = \text{Number of Shares} \times \text{Market Value per Share} \]
Substituting the values:
\[ \text{Total Investment} = 140 \times 110 = ₹15400 \]

5. **Final Answer**:
Therefore, the man should invest **₹15400** to obtain an annual income of ₹1680 from the shares.

### Summary:
The man should invest ₹15400 in shares to achieve his desired annual income.