Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of 11,400 at the end of nine years, how much money did he borrow?

Options

A. 10000
B. 12000
C. 14000
D. 16000

Answer

To find out how much money Adam borrowed, we will calculate the total interest he paid over the nine years based on the different interest rates for each period.

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
Let the amount Adam borrowed be \( P \).

2. **Calculate Interest for the First 2 Years**:
- Interest rate = 6% per annum
- Time = 2 years
- Interest for the first 2 years:
\[ \text{Interest}_1 = P \times \frac{6}{100} \times 2 = \frac{12P}{100} = 0.12P \]

3. **Calculate Interest for the Next 3 Years**:
- Interest rate = 9% per annum
- Time = 3 years
- Interest for the next 3 years:
\[ \text{Interest}_2 = P \times \frac{9}{100} \times 3 = \frac{27P}{100} = 0.27P \]

4. **Calculate Interest for the Last 4 Years**:
- Interest rate = 14% per annum
- Time = 4 years (since total time is 9 years and first 5 years are accounted)
- Interest for the last 4 years:
\[ \text{Interest}_3 = P \times \frac{14}{100} \times 4 = \frac{56P}{100} = 0.56P \]

5. **Total Interest Paid**:
- The total interest paid over 9 years is the sum of the interests from all three periods:
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.12P + 0.27P + 0.56P = 0.95P \]

6. **Set Up the Equation**:
- We know from the problem that the total interest paid is 11,400:
\[ 0.95P = 11,400 \]

7. **Solve for P**:
- To find \( P \), divide both sides by 0.95:
\[ P = \frac{11,400}{0.95} \]
\[ P = 12,000 \]

8. **Conclusion**:
- Therefore, the amount Adam borrowed is \( \text{Rs. } 12,000 \).