A man invests Rs. 4,455 in Rs. 10 shares that are quoted at Rs. 8.25. If the company declares a 12% dividend on face value, what is his annual dividend income?

Introduction / Context:
This problem involves computing the number of shares bought at a quoted market price and then finding the annual dividend using a percentage rate on the face value. It reinforces two important ideas in stock calculations: market price determines how many shares can be purchased, while dividend is calculated on the nominal (face) value of the shares held.

Given Data / Assumptions:

• Total investment = Rs. 4,455.
• Face value of each share = Rs. 10.
• Market price (quoted value) per share = Rs. 8.25.
• Dividend rate = 12% on face value.
• No brokerage is mentioned.

Concept / Approach:
First we find the number of shares purchased by dividing the total amount invested by the market price per share. Then we compute the total nominal value of those shares and apply the 12% dividend rate on this nominal value to obtain the annual dividend income. The main formulas are:
number of shares = total investment / market price per share dividend per share = 12% of face value total dividend = number of shares * dividend per share

Step-by-Step Solution:
Step 1: Number of shares bought = 4455 / 8.25. Step 2: Compute 4455 / 8.25 = 540 shares. Step 3: Face value of each share = Rs. 10, so total nominal value = 540 * 10 = Rs. 5,400. Step 4: Dividend rate = 12% on face value. Step 5: Annual dividend per share = 12% of Rs. 10 = 0.12 * 10 = Rs. 1.20. Step 6: Total annual dividend = 540 * 1.20 = Rs. 648. Step 7: Therefore, the investor receives Rs. 648 per year as dividend.

Verification / Alternative check:
Instead of working per share, we could take 12% of the total nominal value. Nominal value is Rs. 5,400, and 12% of 5,400 is 0.12 * 5400 = Rs. 648, which agrees with our calculation by number of shares. Both methods confirm that Rs. 648 is correct.

Why Other Options Are Wrong:
Rs. 107.04 and Rs. 648.60 do not result from any correct combination of the given values. Rs. 500 and Rs. 540 are lower than 12% of Rs. 5,400. Only Rs. 648 corresponds exactly to 12% of the correct total nominal value determined from the investment and share price.

Common Pitfalls:
Learners may mistakenly assume that the dividend is 12% of the investment (4,455) rather than 12% of the nominal value. Others might use Rs. 8.25 instead of Rs. 10 as the base for the 12% calculation. Always separate market price (used to determine how many shares you get) from face value (used to compute dividends).

Final Answer:
His annual dividend income is Rs. 648.