The difference between the interest received from two different banks on Rs. 5000 for 2 years is Rs. 25. The difference between their rates is :

Options

A. `1%`
B. `2.5%`
C. `0.5%`
D. `0.25%`

Answer

To solve the problem, we need to find the difference between the rates of interest from two banks given that the difference in the interest earned from both banks on a principal amount of Rs. 5000 over 2 years is Rs. 25.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two banks, Bank A and Bank B.
- Principal (P) = Rs. 5000
- Time (T) = 2 years
- Let the rate of interest for Bank A be R1 and for Bank B be R2.
- The difference in interest earned from both banks is Rs. 25.

2. **Formula for Simple Interest**:
- The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
- For Bank A, the interest earned (SI_A) will be:
\[ SI_A = \frac{5000 \times R1 \times 2}{100} \]
- For Bank B, the interest earned (SI_B) will be:
\[ SI_B = \frac{5000 \times R2 \times 2}{100} \]

3. **Setting Up the Equation**:
- According to the problem, the difference in interest is:
\[ SI_A - SI_B = 25 \]
- Substituting the expressions for SI_A and SI_B:
\[ \frac{5000 \times R1 \times 2}{100} - \frac{5000 \times R2 \times 2}{100} = 25 \]

4. **Simplifying the Equation**:
- Factor out common terms:
\[ \frac{5000 \times 2}{100} (R1 - R2) = 25 \]
- Simplifying the left side:
\[ 100 (R1 - R2) = 25 \]

5. **Solving for the Difference in Rates**:
- Divide both sides by 100:
\[ R1 - R2 = \frac{25}{100} = 0.25 \]
- Therefore, the difference between the rates of interest (R1 - R2) is 0.25%.

### Final Answer:
The difference between their rates is **0.25%**.