Prabhat borrowed some money from a bank at` 8%` p.a. simple interest and lended it to Ashish at `12%` p.a. simple interest. If his profit in 2 years is Rs. 320. What sum of money did he borrow?

Options

A. Rs. 2000
B. Rs. 4000
C. Rs. 6000
D. Rs. 3000

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the variables
Let the amount of money Prabhat borrowed from the bank be \( x \).

### Step 2: Calculate the interest earned from Ashish
Prabhat lends the money to Ashish at an interest rate of 12% per annum for 2 years. The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
For Ashish:
- Principal \( P = x \)
- Rate \( R = 12\% \)
- Time \( T = 2 \) years

Thus, the interest earned from Ashish in 2 years is:
\[ \text{Interest from Ashish} = \frac{x \times 12 \times 2}{100} = \frac{24x}{100} = 0.24x \]

### Step 3: Calculate the interest paid to the bank
Prabhat borrowed the money from the bank at an interest rate of 8% per annum for 2 years. Using the same formula:
For the bank:
- Principal \( P = x \)
- Rate \( R = 8\% \)
- Time \( T = 2 \) years

Thus, the interest paid to the bank in 2 years is:
\[ \text{Interest to Bank} = \frac{x \times 8 \times 2}{100} = \frac{16x}{100} = 0.16x \]

### Step 4: Calculate the profit
According to the problem, Prabhat's profit in 2 years is Rs. 320. The profit can be calculated as the difference between the interest earned from Ashish and the interest paid to the bank:
\[ \text{Profit} = \text{Interest from Ashish} - \text{Interest to Bank} \]
Substituting the values we calculated:
\[ 320 = 0.24x - 0.16x \]
\[ 320 = 0.08x \]

### Step 5: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{320}{0.08} \]
Calculating this gives:
\[ x = 320 \times 12.5 = 4000 \]

### Conclusion
Thus, the sum of money Prabhat borrowed from the bank is Rs. 4000.