A man invested ₹ 4455 in ₹ 10 shares quoted at ₹ 8.25. If the rate of dividend be 12%, his annual income is :

### Concept & Calculating Annual Income Annual income is determined by multiplying the number of shares owned by the dividend received per share. The number of shares is found using the investment and market value. $$ \text{Annual Income} = \text{Total Shares} \times \left( \frac{\text{Dividend Rate}}{100} \times \text{Face Value} \right) $$ ### Step-by-Step Solution * **Given:** Investment = ₹ 4455, Face Value = ₹ 10, Market Value = ₹ 8.25, Dividend Rate = 12%. * **Step 1: Calculate the Number of Shares.** Number of shares = $\frac{\text{Total Investment}}{\text{Market Value}} = \frac{4455}{8.25}$. Convert to fraction: $8.25 = \frac{33}{4}$. Number of shares = $4455 \times \frac{4}{33} = 135 \times 4 = 540$ shares. * **Step 2: Calculate Dividend per Share.** Dividend = 12% of Face Value = 12% of ₹ 10 = ₹ 1.20. * **Step 3: Calculate Total Annual Income.** Total Income = $540 \times 1.20 = 648$. ### Exam Strategy & Shortcut Always convert tricky decimals to fractions to avoid messy long division. Turning $8.25$ into $\frac{33}{4}$ turns a difficult division problem into a manageable simplification step. ### Common Pitfall Calculating the 12% dividend based on the market value (₹ 8.25) instead of the face value (₹ 10). Dividend yields are exclusively tied to face value. ### Final Answer Therefore, the correct answer is **₹ 648**.