Nitin borrowed some money at the rate of 6% per annum for the first three years, 9% per annum for the next five years and 13% per annum for the period beyond eight years. If the total amount paid by him at the end of eleven years is Rs 16,160, the money borrowed by him (in Rs.) was

Options

A. Rs 6000
B. Rs 8500
C. Rs 8000
D. None

Answer

To solve the problem, we will calculate the total simple interest accrued over the 11 years and then find the principal amount borrowed by Nitin.

### Step-by-Step Solution:

1. **Identify the time periods and interest rates:**
- For the first 3 years, the interest rate is 6% per annum.
- For the next 5 years (from year 4 to year 8), the interest rate is 9% per annum.
- For the last 3 years (from year 9 to year 11), the interest rate is 13% per annum.

2. **Calculate the total interest for each period:**
- **First 3 years:**
\[ \text{Interest}_1 = P \times \frac{6}{100} \times 3 = 0.18P \]
- **Next 5 years:**
\[ \text{Interest}_2 = P \times \frac{9}{100} \times 5 = 0.45P \]
- **Last 3 years:**
\[ \text{Interest}_3 = P \times \frac{13}{100} \times 3 = 0.39P \]

3. **Calculate the total interest over 11 years:**
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.18P + 0.45P + 0.39P = 1.02P \]

4. **Calculate the total amount paid at the end of 11 years:**
The total amount paid is given as Rs 16,160. The total amount is the sum of the principal and the total interest:
\[ \text{Total Amount} = P + \text{Total Interest} = P + 1.02P = 2.02P \]
\[ 2.02P = 16160 \]

5. **Solve for the principal (P):**
\[ P = \frac{16160}{2.02} = 8000 \]

### Final Answer:
The money borrowed by Nitin was Rs 8000.

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