Rohan borrowed a certain sum of money at simple interest. The rate of interest was 3% per annum for first 3 years, 4% per annum for next 5 years and 6% per annum for next 7 years. If he paid Rs. 2059 as interest, then what is the sum borrowed (in Rs.)?

Options

A. 2400
B. 2500
C. 2900
D. 3100

Answer

To find the sum borrowed by Rohan, we will calculate the total interest paid over the different time periods with their respective rates and set it equal to Rs. 2059.

### Step-by-step Solution:

1. **Define the Principal Amount**:
Let the sum borrowed (principal) be Rs. P.

2. **Calculate Interest for Each Time Period**:
- For the first 3 years at 3% per annum:
\[ \text{Interest}_1 = P \times \frac{3}{100} \times 3 = \frac{9P}{100} \]
- For the next 5 years at 4% per annum:
\[ \text{Interest}_2 = P \times \frac{4}{100} \times 5 = \frac{20P}{100} = \frac{20P}{100} \]
- For the next 7 years at 6% per annum:
\[ \text{Interest}_3 = P \times \frac{6}{100} \times 7 = \frac{42P}{100} \]

3. **Total Interest Calculation**:
Now, we can sum up all the interests calculated:
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = \frac{9P}{100} + \frac{20P}{100} + \frac{42P}{100} = \frac{71P}{100} \]

4. **Set Up the Equation**:
According to the problem, the total interest paid is Rs. 2059:
\[ \frac{71P}{100} = 2059 \]

5. **Solve for P**:
To find P, multiply both sides of the equation by 100:
\[ 71P = 205900 \]
Now, divide both sides by 71:
\[ P = \frac{205900}{71} \]
Performing the division:
\[ P = 2900 \]

Thus, the sum borrowed by Rohan is Rs. 2900.