A man buys 20 shares of Rs 50 each at Rs 5 discount per share. The company declares a dividend of 13.5 percent on the nominal value. What effective rate of interest does he obtain on his investment?

Introduction / Context:
This question is a classic stocks and shares problem that tests your ability to relate nominal value, market price, discount, dividend rate and effective yield. The idea is to compute the return on the actual money invested, not on the face value. Such questions are very common in banking, SSC and other competitive exams under the topic of stocks and shares.

Given Data / Assumptions:

• Number of shares purchased = 20
• Nominal value (face value) of each share = Rs 50
• Shares bought at Rs 5 discount, so market price per share = Rs 50 - Rs 5 = Rs 45
• Dividend declared = 13.5 percent (13.5 percent of nominal value)
• We need the effective rate of interest on the investment.

Concept / Approach:
Dividend is always calculated on nominal value, but the investor actually pays the market price. So we first compute:

• Total nominal value = Number of shares * Nominal value per share.
• Total dividend = Dividend rate * Total nominal value.
• Total investment = Number of shares * Market price per share.

Then effective rate of interest (or yield) is:
Yield (%) = (Annual dividend / Investment) * 100.

Step-by-Step Solution:
Step 1: Nominal value per share = Rs 50. Step 2: Market price per share = Rs 50 - Rs 5 = Rs 45. Step 3: Total nominal value = 20 * 50 = Rs 1000. Step 4: Dividend rate = 13.5 percent, so annual dividend = 1000 * 13.5 / 100 = Rs 135. Step 5: Total investment = 20 * 45 = Rs 900. Step 6: Yield (%) = 135 / 900 * 100 = 15%.
Verification / Alternative check:
We can reduce the fraction 135 / 900. Divide numerator and denominator by 45: 135 / 900 = 3 / 20. Then 3 / 20 * 100 = 15%. This confirms that the effective rate of return is exactly 15 percent on the amount invested, so the chosen option is consistent.

Why Other Options Are Wrong:

• 13%: Slightly lower than the correct yield because it ignores the effect of buying at a discount.
• 12%: Too low; it may come from using an incorrect dividend or investment figure.
• 16%: Slightly higher than the correct yield and does not match the precise calculation.

Common Pitfalls:

• Calculating dividend on the market price instead of on nominal value.
• Forgetting that discount reduces cost, which increases effective yield.
• Incorrectly computing percentage by forgetting to multiply by 100.

Final Answer:
The effective rate of interest obtained on the investment is 15%.