By investing rs 1100 in a `(5)1/2%` stock one earns rs 77. the stock is then quoted at

Options

A. Rs 93
B. Rs 107
C. RS (78)4/7
D. Rs (97)3/4

Answer

To solve the problem step by step, we need to find the quoted price of the stock based on the investment and the earnings.

### Step 1: Understand the given information
We know that:
- Investment = Rs 1100
- Earnings = Rs 77
- Rate of the stock = \(5 \frac{1}{2}\% = \frac{11}{2}\%\)

### Step 2: Calculate the nominal value of the stock
The nominal value of the stock can be calculated using the formula for earnings:
\[ \text{Earnings} = \left(\frac{\text{Nominal Value} \times \text{Rate}}{100}\right) \]
Given that the earnings are Rs 77, we can rearrange the formula to find the nominal value:
\[ 77 = \left(\frac{\text{Nominal Value} \times \frac{11}{2}}{100}\right) \]

### Step 3: Rearranging the formula
To find the nominal value, we can rearrange the equation:
\[ \text{Nominal Value} = \frac{77 \times 100}{\frac{11}{2}} = \frac{77 \times 100 \times 2}{11} \]

### Step 4: Calculate the nominal value
Now, we need to perform the calculation:
\[ \text{Nominal Value} = \frac{15400}{11} = 1400 \]

### Step 5: Calculate the quoted price of the stock
The quoted price of the stock can be found using the investment and the nominal value:
\[ \text{Quoted Price} = \frac{\text{Investment}}{\text{Nominal Value}} \times 100 \]
Substituting the values:
\[ \text{Quoted Price} = \frac{1100}{1400} \times 100 \]

### Step 6: Perform the calculation
Now, we calculate the quoted price:
\[ \text{Quoted Price} = \frac{1100 \times 100}{1400} = \frac{110000}{1400} = 78.57 \]

### Final Answer
The stock is then quoted at Rs 78.57.

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