The compound interest on a sum of money for 2 years is `Rs. 615` and the simple interest for the same period is `Rs. 600`. Find the principal.

Options

A. `Rs.6,500`
B. `Rs.6000`
C. `Rs.8,000`
D. `Rs.9,500`

Answer

To find the principal amount based on the given compound interest (CI) and simple interest (SI) for 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Compound Interest (CI) for 2 years = Rs. 615
- Simple Interest (SI) for 2 years = Rs. 600

2. **Calculate the Difference Between CI and SI:**
\[ \text{Difference} = \text{CI} - \text{SI} = 615 - 600 = 15 \]

3. **Use the Formula to Find the Rate of Interest (r):**
The formula relating CI, SI, and the rate of interest for 2 years is:
\[ \text{CI} - \text{SI} = \frac{\text{SI} \times r}{100} \times 2 \]
Substituting the known values:
\[ 15 = \frac{600 \times r}{100} \times 2 \]

4. **Simplify the Equation:**
\[ 15 = \frac{600 \times r \times 2}{100} \]
\[ 15 = \frac{1200r}{100} \]
\[ 15 = 12r \]

5. **Solve for r:**
\[ r = \frac{15}{12} = 1.25 \]
\[ r = 5\% \quad (\text{since we need the rate per annum}) \]

6. **Use the SI Formula to Find the Principal (P):**
The formula for Simple Interest is:
\[ SI = \frac{P \times r \times t}{100} \]
Rearranging the formula to find P:
\[ P = \frac{SI \times 100}{r \times t} \]
Substituting the known values:
\[ P = \frac{600 \times 100}{5 \times 2} \]

7. **Calculate the Principal:**
\[ P = \frac{60000}{10} = 6000 \]

### Final Answer:
The principal amount is **Rs. 6000**.

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