What is the S.P. of a `7%` stock in which an income of Rs. 250 is derived by investing Rs. 3500. brokerage being `(1/8)%`?

Options

A. Rs. `98 1/8`
B. Rs. `97 7/8`
C. Rs. 98
D. Rs. `107 1/8`

Answer

To find the selling price (S.P.) of a 7% stock given the income and investment details, we can follow these steps:

### Step 1: Understand the given information
- Income from the stock = Rs. 250
- Investment amount = Rs. 3500
- Brokerage = \( \frac{1}{8}\% \)

### Step 2: Calculate the effective investment after brokerage
Brokerage is calculated on the investment amount.

Brokerage = \( \frac{1}{8}\% \) of Rs. 3500
= \( \frac{1}{8} \times \frac{1}{100} \times 3500 \)
= \( \frac{3500}{800} \)
= Rs. 4.375

Now, subtract the brokerage from the investment to find the effective investment:
Effective Investment = Investment - Brokerage
= Rs. 3500 - Rs. 4.375
= Rs. 3495.625

### Step 3: Calculate the nominal value of the stock
The nominal value (N) of the stock can be calculated using the formula:
\[ \text{Income} = \left( \frac{\text{Nominal Value} \times \text{Rate}}{100} \right) \]
Here, the rate is 7%.

Rearranging the formula to find the nominal value:
\[ \text{Nominal Value} = \frac{\text{Income} \times 100}{\text{Rate}} = \frac{250 \times 100}{7} = \frac{25000}{7} \approx 3571.43 \]

### Step 4: Calculate the Selling Price (S.P.)
The Selling Price can be calculated using the effective investment and the nominal value of the stock.

Since the effective investment is Rs. 3495.625, we can find the Selling Price using the formula:
\[ \text{S.P.} = \frac{\text{Effective Investment} \times \text{Nominal Value}}{\text{Nominal Value} - \text{Brokerage}} \]

However, a simpler approach is to find the S.P. directly by using the formula:
\[ \text{S.P.} = \text{Effective Investment} \times \left( \frac{\text{Nominal Value}}{\text{Effective Investment}} \right) \]

We can also use the formula:
\[ \text{S.P.} = \text{Effective Investment} + \text{Brokerage} \]
= Rs. 3495.625 + Rs. 4.375
= Rs. 3500

### Final Answer
Thus, the Selling Price (S.P.) of the 7% stock is approximately Rs. 3500.

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