If an investment of Rs. 42,000 in Rs. 300 shares of a company, paying a dividend of 7%, results in an annual income of Rs. 2100, then find the market value of each share.

Answer

To solve the question step by step, we will follow the mathematical principles related to shares and dividends.

### Step 1: Understand the given information
- Total investment = Rs 42,000
- Face value of each share = Rs 300
- Dividend rate = 7%
- Annual income = Rs 2,100

### Step 2: Calculate the rate of return
The rate of return can be calculated using the formula:
\[ \text{Rate of Return} = \left( \frac{\text{Annual Income}}{\text{Total Investment}} \right) \times 100 \]
Substituting the values:
\[ \text{Rate of Return} = \left( \frac{2100}{42000} \right) \times 100 \]

### Step 3: Simplify the calculation
Calculating the fraction:
\[ \frac{2100}{42000} = \frac{1}{20} \]
Now, multiplying by 100:
\[ \text{Rate of Return} = \frac{1}{20} \times 100 = 5\% \]

### Step 4: Use the relationship between face value, dividend rate, market value, and rate of return
The relationship can be expressed as:
\[ \text{Face Value} \times \text{Dividend Rate} = \text{Market Value} \times \text{Rate of Return} \]
Substituting the known values:
\[ 300 \times 7\% = \text{Market Value} \times 5\% \]
Converting percentages to decimals:
\[ 300 \times 0.07 = \text{Market Value} \times 0.05 \]

### Step 5: Calculate the left side
Calculating:
\[ 300 \times 0.07 = 21 \]
So, we have:
\[ 21 = \text{Market Value} \times 0.05 \]

### Step 6: Solve for Market Value
To find the market value, rearranging the equation gives:
\[ \text{Market Value} = \frac{21}{0.05} \]
Calculating:
\[ \text{Market Value} = 21 \div 0.05 = 420 \]

### Final Answer
The market value of each share is Rs 420.

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