A man invested RS 388 In a stock at 97 to obtain an income of Rs 22. the dividend from the stock is

Options

A. `12%`
B. `3%`
C. `(5)1/2%`
D. `22.68%`

Answer

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

### Step 1: Understand the Investment and Income
The man invested Rs. 388 in a stock priced at Rs. 97 to obtain an income of Rs. 22.

### Step 2: Calculate the Income from Rs. 97 Investment
We need to find out how much income he would earn if he had invested Rs. 97 instead of Rs. 388. We can set up a proportion:
\[ \text{Income from Rs. 97} = \left(\frac{\text{Income from Rs. 388}}{\text{Investment of Rs. 388}}\right) \times \text{Investment of Rs. 97} \]
Substituting the values:
\[ \text{Income from Rs. 97} = \left(\frac{22}{388}\right) \times 97 \]

### Step 3: Perform the Calculation
Now, we calculate the above expression:
\[ \text{Income from Rs. 97} = \left(\frac{22 \times 97}{388}\right) = \frac{2134}{388} \approx 5.50 \]
So, the income from an investment of Rs. 97 is approximately Rs. 5.50.

### Step 4: Calculate the Dividend on Rs. 100 Stock
To find the dividend percentage, we need to determine what the income would be on a Rs. 100 stock. The dividend can be calculated as follows:
\[ \text{Dividend} = \left(\frac{\text{Income from Rs. 97}}{\text{Investment of Rs. 97}}\right) \times 100 \]
Substituting the values:
\[ \text{Dividend} = \left(\frac{5.50}{97}\right) \times 100 \]

### Step 5: Perform the Calculation for Dividend
Now, we calculate the above expression:
\[ \text{Dividend} = \left(\frac{5.50 \times 100}{97}\right) \approx 5.67 \]
This means the dividend on Rs. 100 stock is approximately 5.67%.

### Step 6: Convert to Percentage
To express it as a percentage:
\[ \text{Dividend Percentage} = 5.67\% \]
This can also be expressed as \(5 \frac{2}{3}\%\) or \(5.5\%\) when rounded.

### Final Answer
The dividend from the stock is approximately \(5.5\%\).

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