What is the market value of `4(1)/(2)%` (Rs 100) share, when an investment of Rs 1,800 produces an income of Rs 72?

Answer

To find the market value of a `4(1/2)%` (Rs 100) share, given that an investment of Rs 1,800 produces an income of Rs 72, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Nominal value of each share (N) = Rs 100
- Investment (I) = Rs 1,800
- Income (E) = Rs 72
- Dividend percentage (D) = `4(1/2)%` = `4.5%` = `9/2%`

2. **Calculate the Number of Shares:**
The formula for income from shares is:
\[ \text{Income} = \text{Number of Shares} \times \text{Nominal Value} \times \frac{\text{Dividend Percentage}}{100} \]
Rearranging the formula to find the number of shares (N_shares):
\[ N_{shares} = \frac{E}{N \times \frac{D}{100}} = \frac{72}{100 \times \frac{9}{2 \times 100}} \]
Simplifying this:
\[ N_{shares} = \frac{72}{100 \times \frac{9}{200}} = \frac{72 \times 200}{100 \times 9} = \frac{14400}{900} = 16 \]

3. **Calculate the Market Value of One Share:**
We know that:
\[ \text{Investment} = \text{Market Value} \times \text{Number of Shares} \]
Rearranging to find the market value (M):
\[ M = \frac{I}{N_{shares}} = \frac{1800}{16} \]
Simplifying this:
\[ M = 112.50 \]

### Final Answer:
The market value of one `4(1/2)%` (Rs 100) share is Rs 112.50.

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