A person invests ₹ 5508 in 4% stock at 102. He afterwards sells out at 105 and reinvests in 5% stock at 126. What is the change in his income?

### Concept & Strategy The problem involves a two-step transaction: calculating the initial income, finding the sale proceeds from selling the current stock, and then calculating the new income from the reinvested proceeds. $$ \text{Number of Shares} = \frac{\text{Investment}}{\text{Market Value}} $$ ### Step-by-Step Solution 1. **Calculate Initial Income:** - Investment = ₹ 5508, Market Value = ₹ 102 - Number of shares = $\frac{5508}{102} = 54$ shares. - Face value of 54 shares = $54 \times 100 = 5400$. - Initial Income = 4% of 5400 = $\frac{4}{100} \times 5400 = \text{₹ } 216$. 2. **Calculate Sale Proceeds:** - He sells 54 shares at ₹ 105 each. - Total sale proceeds = $54 \times 105 = \text{₹ } 5670$. 3. **Calculate New Income:** - He reinvests ₹ 5670 in 5% stock at ₹ 126. - New number of shares = $\frac{5670}{126} = 45$ shares. - Face value of 45 shares = $45 \times 100 = 4500$. - New Income = 5% of 4500 = $\frac{5}{100} \times 4500 = \text{₹ } 225$. 4. **Determine Change in Income:** - Change in income = New Income - Initial Income - Change = $225 - 216 = \text{₹ } 9$. ### Exam Strategy & Shortcut Income can be directly calculated as $\text{Income} = \frac{\text{Investment}}{\text{Market Value}} \times \text{Dividend \%}$. Initial Income = $\frac{5508}{102} \times 4 = 216$. Reinvestment Amount = $\frac{5508}{102} \times 105 = 5670$. New Income = $\frac{5670}{126} \times 5 = 225$. Difference = $225 - 216 = 9$. ### Common Pitfall Using the original investment amount (₹ 5508) for the second calculation instead of the updated sale proceeds (₹ 5670) generated by selling at the new market value. ### Final Answer Therefore, the correct answer is **₹ 9**.