Parmeshwarn invested an amount of Rs 12,000 at the rate of 10% per annum simple interest and another amount at the rate of 20% per annum of simple interest. The total interest earned at the end of one year on the total amount invested become 14% per annum. Find the total amount invested.

Options

A. Rs 25,000
B. Rs 20,000
C. Rs 10,000
D. Rs 16,000

Answer

To solve the problem step by step, we will use the concept of simple interest and the allegation method.

### Step 1: Identify the given information
- Amount invested at 10% = Rs 12,000
- Rate of interest for the first investment = 10% per annum
- Rate of interest for the second investment = 20% per annum
- Total interest rate earned = 14% per annum

### Step 2: Calculate the interest from the first investment
Using the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

For the first investment:
\[ \text{Interest from first investment} = \frac{12000 \times 10 \times 1}{100} = 1200 \text{ Rs} \]

### Step 3: Set up the equation for the total interest
Let the amount invested at 20% be \( x \).
The interest from this investment will be:
\[ \text{Interest from second investment} = \frac{x \times 20 \times 1}{100} = \frac{20x}{100} = 0.2x \text{ Rs} \]

### Step 4: Write the equation for total interest
The total interest earned from both investments at the end of one year is:
\[ \text{Total Interest} = \text{Interest from first investment} + \text{Interest from second investment} \]
Thus,
\[ 1200 + 0.2x = 0.14(12000 + x) \]

### Step 5: Simplify the equation
Expanding the right side:
\[ 1200 + 0.2x = 1680 + 0.14x \]

### Step 6: Rearranging the equation
Now, move all terms involving \( x \) to one side and constant terms to the other side:
\[ 1200 - 1680 = 0.14x - 0.2x \]
\[ -480 = -0.06x \]

### Step 7: Solve for \( x \)
Dividing both sides by -0.06:
\[ x = \frac{480}{0.06} = 8000 \text{ Rs} \]

### Step 8: Calculate the total amount invested
The total amount invested is:
\[ \text{Total Amount} = 12000 + x = 12000 + 8000 = 20000 \text{ Rs} \]

### Final Answer
The total amount invested by Parmeshwarn is **Rs 20,000**.

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