a person invests some money in a 4% stock at a 10% discount.he gained rs 300 on selling the stock when it was quoting at a 10% premium.this money was invested in a 3% stock t rs75 and sold at a price of rs80 per stock.how much profit/loss did he make over his initial investment? (a) rs 305 profit (b) rs 320 loss (c) rs 410 profit (d) rs 480 loss

Let the face value of the stock be \( x \).

### Step 1: Buying the stock
The person buys the 4% stock at a 10% discount, so he pays 90% of the face value:
\[
\text{Buying price} = 0.9x
\]
Since the stock provides a 4% dividend, the annual income from the stock is:
\[
\text{Annual income} = 0.04x
\]

### Step 2: Selling the stock
The person sells the stock when it is quoting at a 10% premium, so the selling price is 110% of the face value:
\[
\text{Selling price} = 1.1x
\]
The profit from selling the stock is Rs 300, so the difference between the selling price and the buying price is Rs 300:
\[
1.1x - 0.9x = 300
\]
\[
0.2x = 300
\]
\[
x = \frac{300}{0.2} = 1500
\]
So, the face value of the stock is Rs 1500.

### Step 3: Selling the stock at premium
Now, the person sold the stock at a premium of 10%, so the selling price is:
\[
\text{Selling price} = 1.1 \times 1500 = 1650 \text{ Rs}
\]

### Step 4: Re-investing in a 3% stock
The person invests the Rs 1650 in a 3% stock priced at Rs 75. The number of stocks purchased is:
\[
\text{Number of stocks} = \frac{1650}{75} = 22 \text{ stocks}
\]
Each stock provides a dividend of 3%, so the annual income from the new stock is:
\[
\text{Annual income} = 0.03 \times 75 \times 22 = 49.5 \text{ Rs}
\]

### Step 5: Selling the new stock
The person then sells the 22 stocks at Rs 80 per stock:
\[
\text{Selling price} = 22 \times 80 = 1760 \text{ Rs}
\]

### Step 6: Profit/Loss calculation
The total money initially invested in the 4% stock was:
\[
\text{Initial investment} = 0.9 \times 1500 = 1350 \text{ Rs}
\]
The total amount after selling the 3% stock is Rs 1760. Hence, the total profit is:
\[
\text{Profit} = 1760 - 1350 = 410 \text{ Rs}
\]

Thus, the person made a profit of Rs 410, and the correct answer is **(c) Rs 410 profit**.

---

Do you want details or have any questions?

Here are some related questions to expand your understanding:
1. What is the importance of stock discounts and premiums in real investments?
2. How do dividend rates affect long-term stock returns?
3. What are the risks involved in selling stock at a premium or discount?
4. How would the calculations change if the stock paid no dividend?
5. How can changes in stock prices influence investment decisions?

**Tip**: Always compare the percentage gains or losses relative to your initial investment to understand your returns.

A person invests some money in a 4% stock at a 10% discount. He gained Rs 300 on selling the stock when it was quoting at a 10% premium. This money was invested in a 3% stock at Rs 75 and sold at a price of Rs 80 per stock. How much profit/loss did he make over his initial investment? (a) Rs 305 profit (b) Rs 320 loss (c) Rs 410 profit (d) Rs 480 loss.

Understand how to calculate profit from a stock investment involving a 4% dividend stock bought at a 10% discount and a 3% stock sold at a higher price. This detailed solution covers key formulas and concepts related to percentages, profit/loss, and stock market transactions. Suitable for Grades 9-12.

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