Aman buys Rs 20 shares paying `9%` dividend. The man wants to have an interest of `12%` on his money. The market value of each share must be

Options

A. RS 12
B. Rs 15
C. Rs 18
D. Rs 21

Answer

To solve the problem step by step, we need to find the market value of each share that Aman should buy to achieve a desired interest rate of 12% on his investment.

### Step 1: Calculate the Dividend on Rs 20 Share
The dividend on a share is calculated using the formula:
\[ \text{Dividend} = \left(\frac{\text{Dividend Rate}}{100}\right) \times \text{Face Value} \]
Here, the dividend rate is 9% and the face value of the share is Rs 20.

\[ \text{Dividend} = \left(\frac{9}{100}\right) \times 20 = \frac{180}{100} = 1.8 \]
So, the dividend on a Rs 20 share is Rs 1.8.

### Step 2: Determine the Desired Income
Aman wants to have an interest of 12% on his investment. This means he wants an income of Rs 12 for every Rs 100 invested.

### Step 3: Set Up the Equation for Market Value
Let the market value of each share be \( x \). The income from the share should be equal to the desired income. The formula for the income from the share is:
\[ \text{Income} = \left(\frac{\text{Dividend}}{\text{Market Value}}\right) \times 100 \]
We want this income to be equal to 12% of the market value:
\[ \frac{1.8}{x} \times 100 = 12 \]

### Step 4: Solve for Market Value \( x \)
Rearranging the equation gives:
\[ 1.8 \times 100 = 12x \]
\[ 180 = 12x \]
\[ x = \frac{180}{12} = 15 \]
Thus, the market value of each share must be Rs 15.

### Final Answer
The market value of each share must be Rs 15.

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