Same principal is invested in schemes of compound interest and simple interest. The interest obtained in compound interest and simple interest schemes for two years are Rs 660 and Rs 600 respectively. If the rate of interest is 10%, then what is the principal (in Rs)?

Options

A. 5000
B. 6000
C. 3000
D. 2500

Answer

To solve the problem step by step, we will use the formulas for Simple Interest (SI) and Compound Interest (CI).

### Step 1: Understand the given information
- The interest obtained from the Simple Interest scheme for 2 years is Rs 600.
- The interest obtained from the Compound Interest scheme for 2 years is Rs 660.
- The rate of interest is 10%.

### Step 2: Calculate the Simple Interest for 1 year
Since the Simple Interest for 2 years is Rs 600, the interest for 1 year can be calculated as:
\[ \text{SI for 1 year} = \frac{600}{2} = 300 \text{ Rs} \]

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal
- \( R \) = Rate of interest (10%)
- \( T \) = Time (1 year for our calculation)

For 1 year, we can set up the equation:
\[ 300 = \frac{P \times 10 \times 1}{100} \]

### Step 4: Rearrange the equation to find the Principal
Rearranging the equation gives:
\[ 300 = \frac{10P}{100} \]
Multiplying both sides by 100:
\[ 30000 = 10P \]
Now, divide both sides by 10:
\[ P = \frac{30000}{10} = 3000 \text{ Rs} \]

### Step 5: Verify with Compound Interest
Now, let's verify the principal using Compound Interest. The formula for Compound Interest for 2 years is:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ 660 = 3000 \left(1 + \frac{10}{100}\right)^2 - 3000 \]
Calculating the term inside the parentheses:
\[ 660 = 3000 \left(1.1\right)^2 - 3000 \]
Calculating \( (1.1)^2 = 1.21 \):
\[ 660 = 3000 \times 1.21 - 3000 \]
Calculating \( 3000 \times 1.21 = 3630 \):
\[ 660 = 3630 - 3000 \]
\[ 660 = 630 \]
This confirms that our calculations are consistent.

### Final Answer
The principal amount is:
\[ \boxed{3000 \text{ Rs}} \]