Rs. 3500 was lent partly @ 4% and partly @ 6% SI. The total interest received after 3 years is 498. What is the amount lent @4% SI ?

Options

A. Rs. 1300
B. Rs. 1800
C. Rs. 200
D. Rs.2200

Answer

To solve the problem, we need to determine how much of the total amount of Rs. 3500 was lent at the rate of 4% simple interest. Let's denote:

- The amount lent at 4% as \( x \)
- The amount lent at 6% as \( 3500 - x \)

### Step 1: Set up the equation for total interest

The formula for simple interest is given by:

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

For the amount lent at 4%:
\[ \text{SI}_1 = \frac{x \times 4 \times 3}{100} = \frac{12x}{100} = 0.12x \]

For the amount lent at 6%:
\[ \text{SI}_2 = \frac{(3500 - x) \times 6 \times 3}{100} = \frac{18(3500 - x)}{100} = 0.18(3500 - x) \]

### Step 2: Write the total interest equation

According to the problem, the total interest received after 3 years is Rs. 498. Therefore, we can write the equation:

\[ 0.12x + 0.18(3500 - x) = 498 \]

### Step 3: Simplify the equation

Expanding the equation gives:

\[ 0.12x + 0.18 \times 3500 - 0.18x = 498 \]

Calculating \( 0.18 \times 3500 \):

\[ 0.18 \times 3500 = 630 \]

So, substituting back into the equation:

\[ 0.12x + 630 - 0.18x = 498 \]

Combining like terms:

\[ -0.06x + 630 = 498 \]

### Step 4: Solve for \( x \)

Rearranging the equation:

\[ -0.06x = 498 - 630 \]

Calculating \( 498 - 630 \):

\[ 498 - 630 = -132 \]

So we have:

\[ -0.06x = -132 \]

Dividing both sides by -0.06:

\[ x = \frac{-132}{-0.06} = 2200 \]

### Step 5: Conclusion

The amount lent at the rate of 4% simple interest is \( \boxed{2200} \).