By investing Rs. 1,620 in an 8% stock, Michael earns Rs. 135 as annual dividend. At what market price per Rs. 100 nominal is the stock quoted?

Introduction / Context:
This question examines how to connect the amount of money invested in a stock, the annual dividend received, and the market price of the stock. The stock pays a stated percentage dividend on its nominal value, and the investor's income and investment together allow us to work backward to the quoted market value per Rs. 100 nominal.

Given Data / Assumptions:

• Dividend rate = 8% stock, meaning Rs. 8 dividend per Rs. 100 nominal.
• Total money invested by Michael = Rs. 1,620.
• Annual dividend income = Rs. 135.
• We assume there is no brokerage or other cost.

Concept / Approach:
If the market price per Rs. 100 nominal is P rupees, then investing P rupees buys Rs. 100 nominal of stock and yields dividend of Rs. 8. If the investor puts in K rupees, the total nominal value purchased is (K / P) * 100 and the dividend earned is (K / P) * 8. Setting this equal to the given income allows us to solve for P. The relationship can be written as:
(K / P) * 8 = given income

Step-by-Step Solution:
Step 1: Let P be the market price per Rs. 100 nominal. Step 2: For each P rupees invested, the investor gets Rs. 8 dividend (because the stock is 8% on Rs. 100 nominal). Step 3: Michael invests K = Rs. 1,620. Then his annual dividend income is (1620 / P) * 8. Step 4: Set this equal to the given income: (1620 / P) * 8 = 135. Step 5: Simplify: 1620 * 8 = 135 * P. Step 6: Compute the product: 1620 * 8 = 12,960. Step 7: So 12,960 = 135 * P, hence P = 12,960 / 135 = Rs. 96.

Verification / Alternative check:
If P = Rs. 96, then with Rs. 1,620 Michael buys (1620 / 96) * 100 = Rs. 1,687.50 nominal of stock. The dividend on this nominal value at 8% is 0.08 * 1687.5 = Rs. 135, which matches the given income. Therefore the quoted price of Rs. 96 is correct.

Why Other Options Are Wrong:
At Rs. 80, the dividend would be higher than Rs. 135 because more nominal value could be bought. At Rs. 106 or Rs. 108, the amount of nominal stock purchased would be lower and the dividend would be less than Rs. 135. A price of Rs. 120 would reduce the nominal even further and give still lower income. Only Rs. 96 satisfies the income condition exactly.

Common Pitfalls:
A frequent mistake is to treat 8% as the yield on investment instead of the dividend on nominal value. Another error is attempting to divide income by the dividend rate directly without considering the market price factor. Always form an equation based on income = (investment / market price) * dividend per Rs. 100 nominal.

Final Answer:
The stock is quoted at a market value of Rs. 96 per Rs. 100 nominal.