In order to obtain an annual income of Rs. 650 from a 10% stock quoted at Rs. 96, how much money must an investor invest in the stock?

Introduction / Context:
This question checks understanding of how to compute the amount of money that must be invested in a stock in order to obtain a desired annual income. The key idea is that dividend is based on nominal value while the money actually invested depends on the quoted market price of the stock. We combine both ideas to back-calculate the required investment for a target income.

Given Data / Assumptions:

• Dividend rate = 10% stock, meaning Rs. 10 dividend per Rs. 100 nominal value.
• Market price (quoted value) of the stock = Rs. 96 per Rs. 100 nominal.
• Required annual income from dividends = Rs. 650.
• No brokerage or additional charges are mentioned, so we ignore them.

Concept / Approach:
The annual dividend for Rs. 100 nominal is given directly by the dividend rate. To earn a target dividend, we first find the total nominal value of stock required. Once we know the total nominal value, we multiply by the market price per Rs. 100 nominal to obtain the actual cash investment. The steps are:
1. Use dividend rate to find nominal value required. 2. Use quoted price to convert nominal value into actual investment.

Step-by-Step Solution:
Step 1: Dividend on Rs. 100 nominal at 10% stock = Rs. 10 per year. Step 2: Let the total nominal value of stock purchased be N rupees. Step 3: Then annual dividend = 10% of N = (10 / 100) * N = N / 10. Step 4: We want this dividend to equal the required income of Rs. 650, so N / 10 = 650. Step 5: Therefore N = 650 * 10 = Rs. 6,500 nominal. Step 6: Market price is Rs. 96 per Rs. 100 nominal. So investment per Rs. 100 nominal = Rs. 96. Step 7: For Rs. 6,500 nominal, the actual investment = (6500 / 100) * 96 = 65 * 96 = Rs. 6,240.

Verification / Alternative check:
If the investor puts Rs. 6,240 into the 10% stock at Rs. 96, nominal value purchased is (6240 / 96) * 100 = Rs. 6,500 nominal. The annual dividend on Rs. 6,500 nominal at 10% is 0.10 * 6500 = Rs. 650, which matches the required income. So the calculation is consistent.

Why Other Options Are Wrong:
Rs. 3,100 corresponds to only half the required nominal value and would yield Rs. 325. Rs. 6,500 is the nominal value, not the cash invested. Rs. 9,600 corresponds to buying Rs. 10,000 nominal, giving Rs. 1,000 dividend. Rs. 5,200 represents an incorrect combination of nominal and market price. Only Rs. 6,240 correctly matches the target income of Rs. 650 at the given price and dividend rate.

Common Pitfalls:
Common errors include applying 10% directly on the invested amount (ignoring that dividend is on nominal value) or assuming that Rs. 6,500 must be the investment instead of the nominal value. Another mistake is forgetting to scale nominal value by the quoted price per Rs. 100 when computing the actual cash investment.

Final Answer:
The investor must invest Rs. 6,240 in the 10% stock quoted at Rs. 96 to obtain an income of Rs. 650 per year.