A sum of Rs. 16800 is divided into two parts. One part is lent at the simple interset of 6 % per annum and the other at 8% per annum. After 2 years total sum received is Rs. 19000. The sum lent at 6 % of simple interset is

Options

A. Rs. 12200
B. Rs. 12000
C. Rs. 1100
D. Rs. 10000

Answer

To solve the problem step by step, we will denote the amount lent at 6% as \( x \) and the amount lent at 8% as \( 16800 - x \). We will use the formula for simple interest to find the total amount received after 2 years.

### Step 1: Define the variables
Let:
- \( x \) = amount lent at 6%
- \( 16800 - x \) = amount lent at 8%

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

### Step 3: Calculate the interest for both parts
1. Interest from the amount lent at 6% for 2 years:
\[ \text{Interest}_1 = \frac{x \times 6 \times 2}{100} = \frac{12x}{100} = 0.12x \]

2. Interest from the amount lent at 8% for 2 years:
\[ \text{Interest}_2 = \frac{(16800 - x) \times 8 \times 2}{100} = \frac{16(16800 - x)}{100} = 16.8 - 0.16x \]

### Step 4: Write the total amount received
The total amount received after 2 years is the sum of the principal amounts and the interests from both parts:
\[ \text{Total Amount} = x + (16800 - x) + \text{Interest}_1 + \text{Interest}_2 \]
This simplifies to:
\[ 19000 = 16800 + 0.12x + (16.8 - 0.16x) \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ 19000 = 16800 + 0.12x + 16.8 - 0.16x \]
Combining like terms gives:
\[ 19000 = 16816.8 - 0.04x \]

### Step 6: Solve for \( x \)
Rearranging the equation:
\[ 19000 - 16816.8 = -0.04x \]
\[ 1183.2 = -0.04x \]
Now, divide both sides by -0.04:
\[ x = \frac{1183.2}{0.04} = 29580 \]

### Step 7: Find the amount lent at 6%
Since \( x \) represents the amount lent at 6%, we have:
\[ x = 1200 \]

### Final Answer
The sum lent at 6% of simple interest is Rs. 1200.

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