The difference between the simple interest received from two different banks on Rs. 2000 for 2 years is Rs. 30, the difference between their rates of interest is

Answer

To solve the problem, we need to find the difference between the rates of interest from two banks based on the simple interest they provide on a principal amount of Rs. 2000 over 2 years, with a difference in simple interest of Rs. 30.

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 2000
- Time (T) = 2 years
- Difference in Simple Interest (SI) = Rs. 30

2. **Use the formula for Simple Interest:**
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest.

3. **Calculate Simple Interest for both banks:**
- Let the rate of interest for Bank A be \( R_1 \) and for Bank B be \( R_2 \).
- The Simple Interest from Bank A (SI1) is:
\[ SI_1 = \frac{2000 \times R_1 \times 2}{100} = \frac{4000 \times R_1}{100} = 40R_1 \]
- The Simple Interest from Bank B (SI2) is:
\[ SI_2 = \frac{2000 \times R_2 \times 2}{100} = \frac{4000 \times R_2}{100} = 40R_2 \]

4. **Set up the equation based on the difference in Simple Interest:**
According to the problem, the difference in Simple Interest is Rs. 30:
\[ SI_1 - SI_2 = 30 \]
Substituting the expressions for SI1 and SI2:
\[ 40R_1 - 40R_2 = 30 \]

5. **Factor out the common term:**
\[ 40(R_1 - R_2) = 30 \]

6. **Solve for the difference in rates:**
Divide both sides by 40:
\[ R_1 - R_2 = \frac{30}{40} = \frac{3}{4} \]

7. **Convert to percentage:**
Since the rates are typically expressed in percentage, we convert:
\[ R_1 - R_2 = 0.75\% \]

### Final Answer:
The difference between the rates of interest from the two banks is **0.75%**.