Arun borrowed sum of money from Jayant in the following manner `:`
At 8% for first 4 years,
At 10% for next 6 years.
At 12% for more than 10 years.
He paid a total interest of Rs. 12160 after 15 years . Find the money borrowed by him ?

Answer

To find the amount of money borrowed by Arun from Jayant, we will calculate the simple interest for each period of time at the respective interest rates and then set up an equation based on the total interest paid.

### Step 1: Define the variables
Let the principal amount borrowed by Arun be \( X \).

### Step 2: Calculate the simple interest for each period
1. **For the first 4 years at 8%:**
\[ \text{SI}_1 = \frac{X \times 8 \times 4}{100} = \frac{32X}{100} = 0.32X \]

2. **For the next 6 years at 10%:**
\[ \text{SI}_2 = \frac{X \times 10 \times 6}{100} = \frac{60X}{100} = 0.6X \]

3. **For the remaining 5 years at 12%:**
\[ \text{SI}_3 = \frac{X \times 12 \times 5}{100} = \frac{60X}{100} = 0.6X \]

### Step 3: Sum the simple interests
Now, we can sum the simple interests calculated for each period:
\[ \text{Total Interest} = \text{SI}_1 + \text{SI}_2 + \text{SI}_3 \]
\[ \text{Total Interest} = 0.32X + 0.6X + 0.6X = 1.52X \]

### Step 4: Set up the equation
According to the problem, the total interest paid after 15 years is Rs. 12,160:
\[ 1.52X = 12160 \]

### Step 5: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{12160}{1.52} \]
Calculating the right-hand side:
\[ X = 8000 \]

### Conclusion
The amount of money borrowed by Arun is Rs. 8000.

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