A person lent out a certain sum at 12% p.a. simple interest. In 10 years, the interest was Rs. 2148 more than the sum. The sum was:

Options

A. a) Rs. 10,740
B. b) Rs. 11,540
C. c) Rs. 10,850
D. d) Rs. 10,600

Answer

To solve the problem step by step, we need to find the principal amount (sum) that was lent out at a simple interest rate of 12% per annum. We know that in 10 years, the interest earned was Rs. 2148 more than the principal amount.

### Step 1: Understand the formula for Simple Interest (SI)
The formula for calculating Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount (the sum lent)
- \(R\) = Rate of interest (12% in this case)
- \(T\) = Time (10 years)

### Step 2: Set up the equation
According to the problem, the interest earned in 10 years is Rs. 2148 more than the principal amount. Therefore, we can express this as:
\[ SI = P + 2148 \]

### Step 3: Substitute the values into the SI formula
Substituting the values into the SI formula, we have:
\[ \frac{P \times 12 \times 10}{100} = P + 2148 \]

### Step 4: Simplify the equation
First, simplify the left side:
\[ \frac{120P}{100} = P + 2148 \]
This simplifies to:
\[ 1.2P = P + 2148 \]

### Step 5: Rearrange the equation
Now, rearranging the equation to isolate \(P\):
\[ 1.2P - P = 2148 \]
This simplifies to:
\[ 0.2P = 2148 \]

### Step 6: Solve for \(P\)
Now, divide both sides by 0.2 to find \(P\):
\[ P = \frac{2148}{0.2} \]
Calculating this gives:
\[ P = 10740 \]

### Conclusion
The principal amount (sum) that was lent out is Rs. 10740.