The difference between C.I. and S.I. at a certain rate on rs. 2000 at the end of 2years is rs.12.8. The rate of inerest is:

Options

A. a. 6.8%
B. b. 8%
C. c. 12.8%
D. d. 16.8%

Answer

To find the rate of interest given that the difference between Compound Interest (C.I.) and Simple Interest (S.I.) on Rs. 2000 at the end of 2 years is Rs. 12.8, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The difference between C.I. and S.I. for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \cdot r^2}{100^2} \]
where \( P \) is the principal amount and \( r \) is the rate of interest.

2. **Substitute the Known Values**:
We know:
- Difference = Rs. 12.8
- Principal \( P = Rs. 2000 \)

Substituting these values into the formula gives:
\[ 12.8 = \frac{2000 \cdot r^2}{100^2} \]

3. **Simplify the Equation**:
Rewrite \( 100^2 \) as \( 10000 \):
\[ 12.8 = \frac{2000 \cdot r^2}{10000} \]

To eliminate the fraction, multiply both sides by 10000:
\[ 12.8 \cdot 10000 = 2000 \cdot r^2 \]
\[ 128000 = 2000 \cdot r^2 \]

4. **Solve for \( r^2 \)**:
Divide both sides by 2000:
\[ r^2 = \frac{128000}{2000} \]
\[ r^2 = 64 \]

5. **Find \( r \)**:
To find \( r \), take the square root of both sides:
\[ r = \sqrt{64} \]
\[ r = 8 \]

6. **Conclusion**:
The rate of interest is:
\[ r = 8\% \]

### Final Answer:
The rate of interest is **8%**.