By investing ₹ 3450 in a $4\frac{1}{2}$% stock, a man obtains an income of ₹ 150. Find the market price of the stock.

### Concept & Investment and Income Relationship Total income from an investment is determined by finding the number of shares bought and multiplying by the dividend per share. $$ \text{Total Income} = \left( \frac{\text{Total Investment}}{\text{Market Value}} \right) \times \text{Dividend per Share} $$ ### Step-by-Step Solution * **Given:** Investment = ₹ 3450, Dividend Rate = $4\frac{1}{2}\% = 4.5\%$, Total Income = ₹ 150. Face value is assumed ₹ 100. * **Step 1: Rearrange the formula to solve for Market Value.** $\text{Market Value} = \left( \frac{\text{Total Investment}}{\text{Total Income}} \right) \times \text{Dividend per Share}$ * **Step 2: Substitute the values.** $\text{Market Value} = \left( \frac{3450}{150} \right) \times 4.5$ * **Step 3: Calculate.** $\frac{3450}{150} = 23$ shares. $23 \times 4.5 = 103.50$ ### Exam Strategy & Shortcut First, find the total number of shares purchased by dividing Investment by Market Price, or find the number of shares needed for the income by dividing Total Income by Dividend per share ($150 \div 4.5 = \frac{1500}{45} = \frac{100}{3}$). Then, $\text{Market Value} = \text{Investment} \div \text{Shares} = 3450 \div (\frac{100}{3}) = 34.5 \times 3 = 103.50$. ### Common Pitfall Miscalculating $23 \times 4.5$ under time pressure. Split it up: $(23 \times 4) + (23 \times 0.5) = 92 + 11.5 = 103.50$. ### Final Answer Therefore, the correct answer is **₹ 103.50**.