Durgesh borrowed an amount of Rs. 15,000 at the simple interest rate of 12 p.c.p.a. and another amount at the simple interest rate of 15 p.c. p.a. for a period of two year each. He paid amount of Rs. 9000 as total interest. What is the total amount borrowed?

Options

A. Rs. 18,000
B. Rs. 32000
C. Rs. 35000
D. Rs. 33000

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

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

Where:
- \( P \) = Principal amount (the initial amount borrowed)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Calculate the Simple Interest for the first amount
Durgesh borrowed Rs. 15,000 at a simple interest rate of 12% per annum for 2 years.

Using the formula:
\[ \text{SI}_1 = \frac{15000 \times 12 \times 2}{100} \]

Calculating:
\[ \text{SI}_1 = \frac{15000 \times 12 \times 2}{100} = \frac{360000}{100} = 3600 \]

### Step 2: Let the second amount borrowed be \( x \)
The second amount is borrowed at a simple interest rate of 15% per annum for 2 years.

Using the formula:
\[ \text{SI}_2 = \frac{x \times 15 \times 2}{100} \]

Calculating:
\[ \text{SI}_2 = \frac{x \times 30}{100} = \frac{3x}{10} \]

### Step 3: Set up the equation for total interest
According to the problem, the total interest paid is Rs. 9,000. Therefore, we can write the equation:

\[ \text{SI}_1 + \text{SI}_2 = 9000 \]

Substituting the values we calculated:
\[ 3600 + \frac{3x}{10} = 9000 \]

### Step 4: Solve for \( x \)
First, isolate \( \frac{3x}{10} \):
\[ \frac{3x}{10} = 9000 - 3600 \]
\[ \frac{3x}{10} = 5400 \]

Now, multiply both sides by 10 to eliminate the fraction:
\[ 3x = 54000 \]

Next, divide by 3:
\[ x = \frac{54000}{3} = 18000 \]

### Step 5: Calculate the total amount borrowed
Now that we have both amounts borrowed, we can find the total amount:
\[ \text{Total Amount} = 15000 + x \]
\[ \text{Total Amount} = 15000 + 18000 = 33000 \]

### Final Answer
The total amount borrowed is Rs. 33,000.

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