Raman paid ₹13,300 as simple interest after 9 years. He had borrowed some money at the rate of 6% forfirst two years, at 9% for next three years and at 14% for rest of the period. How much money(in ₹) did he borrow ?

Options

A. 10, 000
B. 14, 000
C. 12, 500
D. 12, 000

Answer

To solve the problem, we need to determine the principal amount (P) that Raman borrowed, given that he paid ₹13,300 as simple interest over 9 years with varying interest rates.

### Step-by-Step Solution:

1. **Identify the Interest Rates and Time Periods:**
- For the first 2 years, the interest rate is 6%.
- For the next 3 years, the interest rate is 9%.
- For the remaining 4 years (9 - 2 - 3 = 4), the interest rate is 14%.

2. **Calculate the Simple Interest for Each Period:**
- **First 2 years:**
\[ \text{SI}_1 = P \times \frac{6}{100} \times 2 = \frac{12P}{100} = 0.12P \]
- **Next 3 years:**
\[ \text{SI}_2 = P \times \frac{9}{100} \times 3 = \frac{27P}{100} = 0.27P \]
- **Last 4 years:**
\[ \text{SI}_3 = P \times \frac{14}{100} \times 4 = \frac{56P}{100} = 0.56P \]

3. **Sum the Simple Interests:**
\[ \text{Total SI} = \text{SI}_1 + \text{SI}_2 + \text{SI}_3 = 0.12P + 0.27P + 0.56P \]
\[ \text{Total SI} = (0.12 + 0.27 + 0.56)P = 0.95P \]

4. **Set Up the Equation:**
Since the total simple interest paid is ₹13,300, we can set up the equation:
\[ 0.95P = 13,300 \]

5. **Solve for P:**
\[ P = \frac{13,300}{0.95} \]
\[ P = 14,000 \]

### Conclusion:
Raman borrowed ₹14,000.