A sum of Rs 15,000 is invested partly at 12% per annum and the remaining at 10% per annum simple interest. If the total interest at the end of 2 years is Rs 3,344. How much money was invested at 10% per annum?

Options

A. Rs 6,200
B. Rs 6,600
C. Rs 6,400
D. Rs 6,500

Answer

To solve the problem, we need to find out how much money was invested at 10% per annum. Let's break down the solution step by step.

### Step 1: Define the Variables
Let:
- \( x \) = amount invested at 10% per annum
- \( 15000 - x \) = amount invested at 12% per annum

### Step 2: Write the Formula for Simple Interest
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = principal amount
- \( R \) = rate of interest
- \( T \) = time in years

### Step 3: Calculate the Interest from Each Investment
1. Interest from the amount invested at 10%:
\[ \text{SI}_{10\%} = \frac{x \times 10 \times 2}{100} = \frac{20x}{100} = 0.2x \]

2. Interest from the amount invested at 12%:
\[ \text{SI}_{12\%} = \frac{(15000 - x) \times 12 \times 2}{100} = \frac{24(15000 - x)}{100} = 24(15000 - x) / 100 \]

### Step 4: Set Up the Equation for Total Interest
According to the problem, the total interest earned at the end of 2 years is Rs 3344. Therefore, we can write:
\[ 0.2x + \frac{24(15000 - x)}{100} = 3344 \]

### Step 5: Simplify the Equation
Multiply through by 100 to eliminate the fraction:
\[ 20x + 24(15000 - x) = 334400 \]
Distributing the 24:
\[ 20x + 360000 - 24x = 334400 \]

### Step 6: Combine Like Terms
Combine the \( x \) terms:
\[ -4x + 360000 = 334400 \]

### Step 7: Isolate \( x \)
Subtract 360000 from both sides:
\[ -4x = 334400 - 360000 \]
\[ -4x = -25600 \]
Now, divide by -4:
\[ x = \frac{-25600}{-4} = 6400 \]

### Step 8: Conclusion
The amount invested at 10% per annum is Rs 6400.