Arun borrowed some money from Jayant. The rate of interest for first 4 years was 8%, for next 6 years. The rate of interest was 10%. per annum and for rest of the years, the rate of interest was 12% per annum. If Arun paid 12,160 simple interest after 15 years then find the total borrowed sum.

Options

A. Rs 10,000
B. Rs 12,000
C. Rs 8,000
D. Rs 15,000

Answer

To solve the problem step by step, we will calculate the total simple interest paid by Arun over the 15 years and then use that to find the principal amount borrowed.

### Step 1: Identify the time periods and interest rates
- For the first 4 years, the interest rate is 8% per annum.
- For the next 6 years (years 5 to 10), the interest rate is 10% per annum.
- For the remaining 5 years (years 11 to 15), the interest rate is 12% per annum.

### Step 2: Calculate the total interest for each period
1. **Interest for the first 4 years:**
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} = P \times \frac{8}{100} \times 4 = 0.32P \]

2. **Interest for the next 6 years:**
\[ \text{Interest} = P \times \frac{10}{100} \times 6 = 0.60P \]

3. **Interest for the last 5 years:**
\[ \text{Interest} = P \times \frac{12}{100} \times 5 = 0.60P \]

### Step 3: Calculate the total interest over 15 years
Now, we add the interest from all three periods:
\[ \text{Total Interest} = 0.32P + 0.60P + 0.60P = 1.52P \]

### Step 4: Set up the equation with the total interest paid
According to the problem, Arun paid a total of 12,160 as simple interest over 15 years:
\[ 1.52P = 12,160 \]

### Step 5: Solve for the principal (P)
To find the principal amount (P), we rearrange the equation:
\[ P = \frac{12,160}{1.52} \]

Calculating this gives:
\[ P = \frac{12,160}{1.52} = 8,000 \]

### Conclusion
The total borrowed sum (principal) is **8,000**.

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