The difference between interest received by A and B is Rs. 18 on Rs. 1500 for 3 year. What is the difference in rate of interest ?

Options

A. `1%`
B. `2.5%`
C. `0.5%`
D. `0.4%`

Answer

To solve the problem, we need to find the difference in the rate of interest between A and B given that the difference in the interest they received is Rs. 18 for a principal amount of Rs. 1500 over 3 years.

### Step-by-Step Solution:

1. **Understand the formula for Simple Interest (SI):**
The formula for calculating simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Calculate the Simple Interest for A:**
Let the rate of interest for A be \( R_1 \).
\[ \text{SI}_A = \frac{1500 \times R_1 \times 3}{100} = \frac{4500R_1}{100} = 45R_1 \]

3. **Calculate the Simple Interest for B:**
Let the rate of interest for B be \( R_2 \).
\[ \text{SI}_B = \frac{1500 \times R_2 \times 3}{100} = \frac{4500R_2}{100} = 45R_2 \]

4. **Set up the equation based on the difference in interest:**
According to the problem, the difference in interest received by A and B is Rs. 18.
\[ \text{SI}_A - \text{SI}_B = 18 \]
Substituting the expressions for SI:
\[ 45R_1 - 45R_2 = 18 \]

5. **Factor out the common term:**
\[ 45(R_1 - R_2) = 18 \]

6. **Solve for the difference in rates:**
Divide both sides by 45:
\[ R_1 - R_2 = \frac{18}{45} \]
Simplifying the fraction:
\[ R_1 - R_2 = \frac{2}{5} = 0.4 \]

7. **Conclusion:**
The difference in the rate of interest between A and B is \( 0.4\% \).