A man invests Rs 1552 in a stock quoted at Rs 97 to earn an annual income of Rs 128. What is the dividend rate of the stock in percent?

Introduction / Context:
In questions on stocks and shares, one of the most common skills tested is the relation between investment, market price, nominal value and dividend percentage. This problem asks for the dividend rate, given how much money is invested, the quoted price of the stock, and the annual income received. Understanding how to convert an investment at a quoted price into nominal value is essential for aptitude and banking exams.

Given Data / Assumptions:

• Total investment = Rs 1552
• Market price of Rs 100 nominal stock = Rs 97 (stock quoted at 97)
• Annual income (dividend received) = Rs 128
• Dividend is paid on nominal (face) value, not on the market price

Concept / Approach:
The key idea is that when stock is quoted at 97, it means a Rs 100 nominal share costs Rs 97 in the market. First we find the total nominal value of stock purchased using investment and market price. Then we apply the standard formula:
Dividend rate (%) = (Annual income / Nominal value) * 100.
This gives the required percentage return declared by the company on the face value.

Step-by-Step Solution:
Step 1: Market price of Rs 100 nominal stock = Rs 97. Step 2: Nominal value purchased = (Investment / Market price) * 100. Step 3: Nominal value = (1552 / 97) * 100 = 1600. Step 4: Dividend is paid on nominal value, so annual dividend = 128. Step 5: Dividend rate (%) = (128 / 1600) * 100 = 8%.
Verification / Alternative check:
If the dividend rate is 8%, then dividend on Rs 1600 nominal value is 1600 * 8 / 100 = Rs 128, which matches the given income. This confirms that the computed rate is consistent with the information provided.

Why Other Options Are Wrong:

• 8.5%: This would give income 1600 * 8.5 / 100 = Rs 136, which is higher than Rs 128.
• 7.5%: This would give income 1600 * 7.5 / 100 = Rs 120, which is less than Rs 128.
• 9%: This would give income 1600 * 9 / 100 = Rs 144, which does not match the given income.

Common Pitfalls:

• Using the market value instead of nominal value to compute dividend.
• Confusing the quoted price 97 with 97% dividend, which is incorrect.
• Forgetting to multiply by 100 when converting the fraction to a percentage.

Final Answer:
The correct dividend rate of the stock is 8%.