X borrowed some money from a source at `8%` simple interest and lent it to Y at `12%` simple interest on the same day and gained ₹4,800 after 3 years. The amount X borrowed, in ₹, is

Options

A. 42000
B. 60000
C. 1,20,000
D. 40000

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
X borrows money at an interest rate of 8% and lends it to Y at an interest rate of 12%. After 3 years, X makes a profit of ₹4,800. We need to find out how much money X borrowed.

### Step 2: Define Variables
Let the amount borrowed by X be \( P \) (in ₹).

### Step 3: Calculate Interest Earned by X
The interest earned by X from lending to Y can be calculated using the formula for simple interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = principal amount (the amount borrowed)
- \( R \) = rate of interest (12% for Y)
- \( T \) = time (3 years)

So, the interest earned by X from Y after 3 years is:
\[ \text{Interest from Y} = \frac{P \times 12 \times 3}{100} = \frac{36P}{100} = 0.36P \]

### Step 4: Calculate Interest Paid by X
The interest paid by X to the source can also be calculated using the same formula:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( R \) = rate of interest (8% for the source)

So, the interest paid by X to the source after 3 years is:
\[ \text{Interest to source} = \frac{P \times 8 \times 3}{100} = \frac{24P}{100} = 0.24P \]

### Step 5: Calculate Profit
The profit made by X is the difference between the interest earned from Y and the interest paid to the source:
\[ \text{Profit} = \text{Interest from Y} - \text{Interest to source} \]
Substituting the values we calculated:
\[ \text{Profit} = 0.36P - 0.24P = 0.12P \]

### Step 6: Set Up the Equation
According to the problem, the profit is ₹4,800. Therefore, we can set up the equation:
\[ 0.12P = 4800 \]

### Step 7: Solve for P
To find \( P \), we can rearrange the equation:
\[ P = \frac{4800}{0.12} \]
Calculating this gives:
\[ P = 40000 \]

### Conclusion
The amount X borrowed is ₹40,000.