A retired man sells out ₹ 7500 of a 10% stock at ₹ 105.50 and invests the proceeds in 14% stock at ₹ 124.50. What is the change in income if he pays a service charge of 0.5% of the face value on each transaction?

### Concept & Logic The net sale proceeds depend on the market value minus any service charges (brokerage). Conversely, the net purchase price is the market value plus service charges. $$ \text{Proceeds} = \text{No. of Shares} \times (\text{Sale Price} - \text{Brokerage}) $$ $$ \text{Investment} = \text{No. of Shares} \times (\text{Purchase Price} + \text{Brokerage}) $$ ### Step-by-Step Solution 1. **Calculate Initial Income:** - Face Value = ₹ 7500 - Dividend = 10% - Initial Income = 10% of 7500 = ₹ 750 2. **Calculate Sale Proceeds:** - Number of shares sold = $\frac{7500}{100} = 75$ - Service charge = 0.5% of Face Value (₹ 100) = ₹ 0.50 per share - Effective selling price per share = $105.50 - 0.50 = \text{₹ } 105$ - Total proceeds = $75 \times 105 = \text{₹ } 7875$ 3. **Calculate New Investment & Income:** - He invests ₹ 7875 in 14% stock at ₹ 124.50. - Effective purchase price per share = $124.50 + 0.50 = \text{₹ } 125$ - Number of shares bought = $\frac{7875}{125} = 63$ - New Face Value = $63 \times 100 = \text{₹ } 6300$ - New Income = 14% of 6300 = ₹ 882 4. **Determine Change in Income:** - Change in Income = $882 - 750 = \text{₹ } 132$ ### Exam Strategy & Shortcut Work with per-share values. Sale realization per share = $105.50 - 0.50 = 105$. Total proceeds = $\frac{7500}{100} \times 105 = 7875$. Cost per new share = $124.50 + 0.50 = 125$. Total new shares = $\frac{7875}{125} = 63$. New income = $63 \times 14 = 882$. Change = $882 - 750 = 132$. ### Common Pitfall Calculating the 0.5% service charge on the market value instead of the face value as explicitly stated in the problem. ### Final Answer Therefore, the correct answer is **₹ 132**.