Find the cost of Rs. 12600 railway stock at (150)1/2 (dividend `(5)1/2%`)

Options

A. Rs 18963
B. Rs 19863
C. Rs 18933
D. none of these

Answer

To find the cost of Rs. 12600 railway stock at (150)1/2 with a dividend of (5)1/2%, we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
First, we need to convert the mixed numbers into improper fractions for easier calculations.

- The stock price of (150)1/2 can be converted as follows:
\[ 150 \frac{1}{2} = \frac{150 \times 2 + 1}{2} = \frac{300 + 1}{2} = \frac{301}{2} \]

- The dividend of (5)1/2 can be converted similarly:
\[ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

### Step 2: Calculate the cost of the stock
The cost of the stock can be calculated using the formula:
\[ \text{Cost of stock} = \text{Nominal Value} \times \frac{\text{Market Price}}{100} \]
Where:
- Nominal Value = Rs. 12600
- Market Price = \(150 \frac{1}{2} = \frac{301}{2}\)

Substituting the values:
\[ \text{Cost of stock} = 12600 \times \frac{301/2}{100} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ \text{Cost of stock} = 12600 \times \frac{301}{2} \times \frac{1}{100} \]
\[ = 12600 \times \frac{301}{200} \]

### Step 4: Perform the multiplication
Now, we will perform the multiplication:
\[ = \frac{12600 \times 301}{200} \]

### Step 5: Calculate the result
Now, we can calculate:
\[ 12600 \div 200 = 63 \]
So,
\[ \text{Cost of stock} = 63 \times 301 \]

### Step 6: Final calculation
Now, we will calculate \(63 \times 301\):
\[ 63 \times 301 = 18963 \]

### Conclusion
Thus, the cost of Rs. 12600 railway stock at (150)1/2 with a dividend of (5)1/2% is Rs. 18963.