A dividend of `12%` was declared on `150rs` shares selling at a certain price. If the rate of return is `10%` calculate
(i) the market value of the shares
(ii) the amount to be invested to obtain an annual dividend of `1350rs`

Answer

Let's solve the problem step by step.

**Given:**
- Nominal value of shares = ₹150
- Dividend declared = 12%
- Rate of return (ROR) = 10%

### (i) Calculate the market value of the shares

1. **Understand the relationship between dividend, nominal value, and market value:**
The formula relating these values is:
\[ \text{Dividend on Nominal Value} = \text{Rate of Return} \times \text{Market Value} \]

2. **Calculate the dividend amount on the nominal value:**
\[ \text{Dividend} = \text{Nominal Value} \times \left(\frac{\text{Dividend \%}}{100}\right) \]
\[ \text{Dividend} = 150 \times \left(\frac{12}{100}\right) = 150 \times 0.12 = ₹18 \]

3. **Set up the equation using the ROR:**
\[ 18 = 10\% \text{ of Market Value} \]
This can be rewritten as:
\[ 18 = \frac{10}{100} \times \text{Market Value} \]

4. **Solve for Market Value:**
\[ 18 = 0.1 \times \text{Market Value} \]
\[ \text{Market Value} = \frac{18}{0.1} = ₹180 \]

### (ii) Calculate the amount to be invested to obtain an annual dividend of ₹1350

1. **Determine the dividend per share:**
From the previous calculation, we found that the dividend per share is ₹18.

2. **Calculate how many shares are needed to earn ₹1350:**
\[ \text{Number of shares} = \frac{\text{Total Dividend Required}}{\text{Dividend per Share}} = \frac{1350}{18} = 75 \]

3. **Calculate the total amount to be invested:**
Since each share is valued at the market price of ₹180:
\[ \text{Total Investment} = \text{Number of Shares} \times \text{Market Value} \]
\[ \text{Total Investment} = 75 \times 180 = ₹13500 \]

### Final Answers:
(i) The market value of the shares is ₹180.
(ii) The amount to be invested to obtain an annual dividend of ₹1350 is ₹13500.

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