The market value of a 10.5% stock, in which an income of ₹ 756 is derived by investing ₹ 9000, brokerage being $\frac{1}{4}$%, is

### Concept & Formula The income derived from a stock is based on its face value, but the actual investment includes the market value plus any brokerage fees. The total investment required to get a certain income is given by: $$ \text{Investment} = \frac{\text{Total Income}}{\text{Dividend \%}} \times (\text{Market Value} + \text{Brokerage}) $$ ### Step-by-Step Solution 1. **Given:** - Dividend % = 10.5% - Total Income = ₹ 756 - Total Investment = ₹ 9000 - Brokerage = $\frac{1}{4}\% = ₹ 0.25$ per ₹ 100 face value. 2. **Determine the cost of ₹ 100 stock:** - Let the cost of a ₹ 100 stock (Market Value + Brokerage) be $x$. - For an investment of $x$, the income is ₹ 10.5. - For an investment of ₹ 9000, the income is: $\frac{10.5}{x} \times 9000 = 756$ 3. **Solve for $x$:** - $x = \frac{10.5 \times 9000}{756}$ - $x = \frac{94500}{756} = 125$ 4. **Calculate the Market Value:** - Cost of stock = Market Value + Brokerage - $125 = \text{Market Value} + 0.25$ - $\text{Market Value} = 125 - 0.25 = 124.75$ ### Exam Strategy & Shortcut Find the cost per unit of income: $\text{Cost} = \frac{\text{Investment}}{\text{Income}} = \frac{9000}{756}$. Then multiply by the dividend rate: $\frac{9000}{756} \times 10.5 = 125$. Subtract brokerage to find market value: $125 - 0.25 = 124.75$. ### Common Pitfall Forgetting to subtract the brokerage from the total cost price of the stock. The calculated value of 125 is the purchase price, not the market value. ### Final Answer Therefore, the correct answer is **₹ 124.75**.