A man invested ₹ 1552 in a stock at 97 to obtain an income of ₹ 128. The dividend from the stock is

### Concept & Finding the Dividend Rate The dividend rate is the income generated per share, expressed as a percentage of the standard face value (₹ 100). First, find the number of shares, then find income per share. $$ \text{Dividend Rate} = \left( \frac{\text{Total Income}}{\text{Number of Shares}} \right) $$ ### Step-by-Step Solution * **Given:** Total Investment = ₹ 1552, Market Value = ₹ 97, Total Income = ₹ 128. * **Step 1: Calculate the number of shares.** Shares = $\frac{\text{Total Investment}}{\text{Market Value}} = \frac{1552}{97}$. $1552 \div 97 = 16$ shares. * **Step 2: Calculate Income per Share.** Income per share = $\frac{\text{Total Income}}{\text{Total Shares}} = \frac{128}{16} = 8$. * **Step 3: Determine Dividend Percentage.** Since the standard face value is ₹ 100, an income of ₹ 8 per share equals an 8% dividend rate. ### Exam Strategy & Shortcut Look at the units digit to help with the division $\frac{1552}{97}$. What number times 7 ends in 2? 6. So the answer is likely to end in 6. 16 is a perfect guess. $16 \times 100 = 1600$, and $16 \times 3 = 48$, $1600 - 48 = 1552$. Perfect. ### Common Pitfall Dividing total income by total investment ($\frac{128}{1552}$) which yields the interest/yield rate, not the dividend rate declared by the company. ### Final Answer Therefore, the correct answer is **8%**.