Same principal is invested in schemes of compound interest and simple interest. The interest obtained in compound interest and simple interest schemes after 2 years are Rs 3520 and Rs 3200 respectively. If the rate of interest is 20%, then what is the principal (in Rs)?

Options

A. 4000
B. 8000
C. 5000
D. 10000

Answer

To solve the problem, we need to find the principal amount (P) invested in both the compound interest and simple interest schemes, given the interest amounts obtained from each scheme after 2 years and the rate of interest.

### Step-by-Step Solution:

1. **Identify the given information**:
- Interest from Simple Interest (SI) after 2 years = Rs 3200
- Interest from Compound Interest (CI) after 2 years = Rs 3520
- Rate of interest (R) = 20% per annum
- Time (T) = 2 years

2. **Use the formula for Simple Interest**:
The formula for calculating Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

3. **Substitute the known values into the formula**:
We can substitute the values we know into the formula:
\[ 3200 = \frac{P \times 20 \times 2}{100} \]

4. **Simplify the equation**:
First, calculate \( 20 \times 2 = 40 \):
\[ 3200 = \frac{P \times 40}{100} \]
Now, multiply both sides by 100 to eliminate the fraction:
\[ 3200 \times 100 = P \times 40 \]
This simplifies to:
\[ 320000 = P \times 40 \]

5. **Solve for P**:
Now, divide both sides by 40 to find the principal:
\[ P = \frac{320000}{40} \]
Calculating this gives:
\[ P = 8000 \]

6. **Conclusion**:
The principal amount invested is Rs 8000.

### Final Answer:
The principal (P) is Rs 8000.