Amount of simple interest earned in 7 years by Arun on the sum invested is Rs. 26000. If the rate of interest was 10% for first 2 years, 12% for next 2 years and 20% for remaining years then find the sum invested

Options

A. Rs. 25000
B. Rs. 30000
C. Rs. 35000
D. Rs. 20000

Answer

To find the sum invested by Arun, we need to calculate the total simple interest earned over 7 years using the different rates for each period.

### Step-by-Step Solution:

1. **Identify the given values**:
- Total Simple Interest (SI) = Rs. 26,000
- Time periods and rates:
- First 2 years: Rate = 10%
- Next 2 years: Rate = 12%
- Remaining 3 years: Rate = 20%

2. **Let the principal amount be \( P \)**.

3. **Calculate the simple interest for each time period**:
- For the first 2 years at 10%:
\[ SI_1 = \frac{P \times 10 \times 2}{100} = \frac{20P}{100} = \frac{P}{5} \]

- For the next 2 years at 12%:
\[ SI_2 = \frac{P \times 12 \times 2}{100} = \frac{24P}{100} = \frac{6P}{25} \]

- For the remaining 3 years at 20%:
\[ SI_3 = \frac{P \times 20 \times 3}{100} = \frac{60P}{100} = \frac{3P}{5} \]

4. **Combine the simple interests**:
\[ Total \, SI = SI_1 + SI_2 + SI_3 \]
\[ Total \, SI = \frac{P}{5} + \frac{6P}{25} + \frac{3P}{5} \]

5. **Find a common denominator to combine the fractions**:
- The common denominator for 5 and 25 is 25.
- Convert each term:
\[ \frac{P}{5} = \frac{5P}{25} \]
\[ \frac{3P}{5} = \frac{15P}{25} \]
- Now, combine:
\[ Total \, SI = \frac{5P}{25} + \frac{6P}{25} + \frac{15P}{25} = \frac{(5P + 6P + 15P)}{25} = \frac{26P}{25} \]

6. **Set the total simple interest equal to Rs. 26,000**:
\[ \frac{26P}{25} = 26000 \]

7. **Solve for \( P \)**:
\[ 26P = 26000 \times 25 \]
\[ 26P = 650000 \]
\[ P = \frac{650000}{26} = 25000 \]

### Final Answer:
The sum invested by Arun is Rs. 25,000.