A man bought 20 shares of Rs. 50 at 5 discount the rate of dividend being `(4)3/4%` .the rate of invest obtained is

Options

A. `(4)3/4%`
B. `(3)1/4%`
C. `5.28%`
D. `4.95%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the investment
The man bought 20 shares at a face value of Rs. 50 each, but he received a discount of Rs. 5 on each share.

- **Face value of one share** = Rs. 50
- **Discount on one share** = Rs. 5
- **Price paid for one share** = Face value - Discount = 50 - 5 = Rs. 45

Now, calculate the total investment:
- **Total investment** = Number of shares × Price paid per share
- Total investment = 20 × 45 = Rs. 900

### Step 2: Calculate the face value of the shares
The total face value of the shares can be calculated as follows:
- **Total face value** = Number of shares × Face value of one share
- Total face value = 20 × 50 = Rs. 1000

### Step 3: Calculate the dividend
The rate of dividend is given as \(4 \frac{3}{4}\%\), which can be converted into an improper fraction:
- \(4 \frac{3}{4}\% = \frac{19}{4}\%\)

Now, calculate the dividend:
- **Dividend** = (Rate of dividend × Total face value) / 100
- Dividend = \(\frac{19}{4} \times 1000 / 100\)
- Dividend = \(\frac{19}{4} \times 10 = \frac{190}{4} = 47.5\)

### Step 4: Calculate the rate of investment obtained
The rate of investment obtained can be calculated using the formula:
- **Rate of investment** = (Dividend / Total investment) × 100
- Rate of investment = (47.5 / 900) × 100

Now, calculate the rate of investment:
- Rate of investment = \( \frac{4750}{900} \approx 5.28\%\)

### Final Answer
The rate of investment obtained is approximately **5.28%**.

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