Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next six years and 12% per annum for the period beyond ten years. If he pays a total of 12,160 as interest only at the end of 15 years, how much money did he borrow?

Options

A. 8000
B. 10000
C. 12000
D. 9000

Answer

To solve the problem step by step, we will calculate the total interest paid over the 15 years based on the different interest rates for each period.

### Step 1: Define the Principal Amount
Let the principal amount borrowed by Arun be \( x \).

### Step 2: Calculate Interest for the First 4 Years
The interest rate for the first 4 years is 8% per annum. The interest for this period can be calculated using the formula for simple interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
For the first 4 years:
\[ \text{Interest}_1 = x \times \frac{8}{100} \times 4 = \frac{32x}{100} = 0.32x \]

### Step 3: Calculate Interest for the Next 6 Years
The interest rate for the next 6 years is 10% per annum. The interest for this period is:
\[ \text{Interest}_2 = x \times \frac{10}{100} \times 6 = \frac{60x}{100} = 0.6x \]

### Step 4: Calculate Interest for the Last 5 Years
The interest rate for the last 5 years (beyond 10 years) is 12% per annum. The interest for this period is:
\[ \text{Interest}_3 = x \times \frac{12}{100} \times 5 = \frac{60x}{100} = 0.6x \]

### Step 5: Calculate Total Interest Over 15 Years
Now, we can sum up all the interest amounts:
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.32x + 0.6x + 0.6x = 1.52x \]

### Step 6: Set Up the Equation
According to the problem, the total interest paid after 15 years is 12,160. Therefore, we set up the equation:
\[ 1.52x = 12,160 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides of the equation by 1.52:
\[ x = \frac{12,160}{1.52} \]
Calculating this gives:
\[ x = 8,000 \]

### Conclusion
The amount of money Arun borrowed is \( \boxed{8000} \).