To produce an annual income of rs 500 in a `4%` stock at 90. the amount of stock needed is

Options

A. Rs 11250
B. Rs 12500
C. Rs 18000
D. Rs 20000

Answer

To solve the problem of determining the amount of stock needed to produce an annual income of Rs. 500 in a 4% stock at 90, we can follow these steps:

### Step 1: Understand the terms
- **Annual Income**: This is the income we want to generate, which is Rs. 500.
- **Rate of Stock**: The stock has a rate of 4%, which means for every Rs. 100 invested in this stock, the annual income is Rs. 4.
- **Market Price of Stock**: The stock is priced at Rs. 90.

### Step 2: Calculate the amount of stock needed to generate Rs. 500
To find out how much stock is needed, we can use the formula for annual income from stock:

\[ \text{Annual Income} = \left(\frac{\text{Amount of Stock} \times \text{Rate of Stock}}{100}\right) \]

Let \( x \) be the amount of stock needed. Then we can set up the equation:

\[ 500 = \left(\frac{x \times 4}{100}\right) \]

### Step 3: Solve for \( x \)
Rearranging the equation to solve for \( x \):

\[ 500 = \frac{4x}{100} \]

Multiply both sides by 100 to eliminate the fraction:

\[ 50000 = 4x \]

Now, divide both sides by 4:

\[ x = \frac{50000}{4} = 12500 \]

### Step 4: Calculate the number of shares needed
Now that we have the amount of stock needed, we can calculate how many shares we need to buy at the market price of Rs. 90:

\[ \text{Number of shares} = \frac{\text{Amount of Stock}}{\text{Market Price}} = \frac{12500}{90} \]

Calculating this gives:

\[ \text{Number of shares} \approx 138.89 \]

Since we cannot buy a fraction of a share, we would need to round up to the nearest whole number, which means we need to buy 139 shares.

### Final Answer
To produce an annual income of Rs. 500 in a 4% stock at 90, the amount of stock needed is Rs. 12,500, and you would need to purchase approximately 139 shares.

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