A invested some money in `4%` stock att 96. now B want to invest in an equally goods `5%` stock. B must purchase a stock worth of

Options

A. Rs 120
B. Rs 124
C. Rs 76.80
D. Rs 80

Answer

To solve the problem step by step, we need to determine how much B must invest in a 5% stock to achieve the same income that A earns from a 4% stock.

### Step 1: Determine A's Income from the 4% Stock
A invested in a 4% stock at a price of 96. The income from the stock can be calculated as follows:

\[ \text{Income from A's investment} = \text{Investment} \times \text{Rate of Return} \]

Let’s assume A invested an amount \( P \). The income from A's investment can be expressed as:

\[ \text{Income} = P \times \frac{4}{100} \]

### Step 2: Calculate the Investment Amount (P)
Since A bought the stock at 96, we can express the investment in terms of the price of the stock:

\[ P = \frac{\text{Investment Amount}}{\text{Price of Stock}} = \frac{P}{96} \]

### Step 3: Set Up the Equation for B's Investment
B wants to invest in a 5% stock. To find out how much B needs to invest to get the same income as A, we set up the equation:

\[ \text{Income from B's investment} = \text{Investment} \times \frac{5}{100} \]

Let’s denote B's investment as \( I \). We want B's income to be equal to A's income:

\[ I \times \frac{5}{100} = P \times \frac{4}{100} \]

### Step 4: Substitute for P
From step 1, we know that:

\[ P = \frac{\text{Income from A}}{\frac{4}{100}} = \frac{I \times \frac{5}{100}}{\frac{4}{100}} \]

### Step 5: Solve for B's Investment (I)
Now, substituting the value of P into the equation:

\[ I \times \frac{5}{100} = \left(\frac{I \times \frac{5}{100}}{\frac{4}{100}}\right) \times \frac{4}{100} \]

This simplifies to:

\[ I = \frac{96 \times 5}{4} \]

Calculating this gives:

\[ I = \frac{480}{4} = 120 \]

### Step 6: Final Calculation
Now, we need to calculate the total investment amount for B to achieve the same income:

\[ I = \frac{96 \times 5}{4} = 120 \]

### Conclusion
Thus, B must purchase a stock worth of **Rupees 120**.

---