Find the market value of 12% Rs 25 shares of a company which pays a dividend of Rs 1,875 on an investment of Rs 20,000

Answer

To find the market value of 12% Rs 25 shares of a company that pays a dividend of Rs 1,875 on an investment of Rs 20,000, we can follow these steps:

### Step 1: Understand the given information
- Dividend percentage = 12%
- Nominal value of each share (N.V.) = Rs 25
- Annual dividend received = Rs 1,875
- Total investment = Rs 20,000

### Step 2: Write the formula for annual dividend
The formula for annual dividend is:
\[ \text{Annual Dividend} = \left(\frac{\text{Dividend Percentage}}{100}\right) \times \text{Nominal Value} \times \text{Number of Shares} \]

### Step 3: Substitute the known values into the formula
We can express the number of shares in terms of the investment and market value:
\[ \text{Number of Shares} = \frac{\text{Investment}}{\text{Market Value}} \]
Thus, substituting this into the dividend formula gives:
\[ 1,875 = \left(\frac{12}{100}\right) \times 25 \times \left(\frac{20,000}{\text{Market Value}}\right) \]

### Step 4: Simplify the equation
Now we can simplify the equation:
\[ 1,875 = \left(0.12\right) \times 25 \times \left(\frac{20,000}{\text{Market Value}}\right) \]
Calculating \(0.12 \times 25\):
\[ 0.12 \times 25 = 3 \]
So the equation becomes:
\[ 1,875 = 3 \times \left(\frac{20,000}{\text{Market Value}}\right) \]

### Step 5: Rearranging the equation
Rearranging gives:
\[ \text{Market Value} = 3 \times \left(\frac{20,000}{1,875}\right) \]

### Step 6: Calculate the market value
Now, calculate \( \frac{20,000}{1,875} \):
\[ \frac{20,000}{1,875} = 10.67 \quad (\text{approximately}) \]
Now multiply by 3:
\[ \text{Market Value} = 3 \times 10.67 \approx 32 \]

### Final Answer
Thus, the market value of each share is approximately Rs 32.

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