A 6% stock yields an 8% return on the investor's money. What is the market value (price per Rs. 100 nominal) of this stock?

Introduction / Context:
Questions on stocks and shares often test the relationship between the nominal (face) value of a share, its dividend rate, the market value, and the effective yield on an investor's money. Here, we are given the dividend rate of the stock and the yield actually obtained by the investor, and we are asked to find the market value of the stock that produces such a yield.

Given Data / Assumptions:

• The nominal (face) value of the stock is taken as Rs. 100.
• The dividend rate on the stock is 6% per year.
• The investor's yield on investment is 8% per year.
• We assume standard convention that a 6% stock means Rs. 6 dividend per year on Rs. 100 nominal value.

Concept / Approach:
For a stock, dividend is always calculated on the nominal value, while yield is calculated on the actual money invested (market value). If the annual dividend on Rs. 100 nominal is D and the market price is P, then the yield on investment is given by:
yield % = (D / P) * 100 In this problem we know the dividend rate (6%) and the yield (8%). We use the above formula to solve for the unknown market value P.

Step-by-Step Solution:
Step 1: Take the nominal value of the stock as Rs. 100. Step 2: Since it is a 6% stock, annual dividend on Rs. 100 nominal is D = 6% of 100 = Rs. 6. Step 3: Let P be the market value (price) of this Rs. 100 stock. Step 4: Given that the yield on investment is 8%, we write: (6 / P) * 100 = 8. Step 5: Simplify: 6 / P = 8 / 100 = 0.08. Step 6: Therefore, P = 6 / 0.08 = 75. Step 7: Thus the market value of the Rs. 100 stock must be Rs. 75.

Verification / Alternative check:
If the stock is bought at Rs. 75 and pays Rs. 6 as annual dividend, then the actual yield is:
yield % = (6 / 75) * 100 = 8% This agrees exactly with the given yield in the problem, so our answer is consistent.

Why Other Options Are Wrong:
Rs. 48 would give a yield of (6 / 48) * 100 = 12.5%, which is greater than 8%, so it is not correct. Rs. 96 would give a yield of (6 / 96) * 100 = 6.25%, which is less than 8%. Rs. 133.33 would produce an even smaller yield of about 4.5%. Rs. 50 would give a yield of 12%, also inconsistent. Only Rs. 75 satisfies the required 8% yield.

Common Pitfalls:
Students sometimes confuse the dividend rate with the yield on investment and try to apply 8% on Rs. 100 directly. Another frequent mistake is to assume that the market value must exceed the nominal value, which is not always true. It is important to remember that dividend is calculated on nominal value, while yield is calculated based on the current market price actually paid by the investor.

Final Answer:
The market value of the stock is Rs. 75 per Rs. 100 nominal value.