The difference between two simple interest on 1350 at different rates in 3 years is Rs 40.5 then find the difference of rate of interest?

Options

A. `0.5%`
B. `2%`
C. `1%`
D. `1.5%`

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the information provided in the question.

### Step 1: Understand the given information
We are given:
- Principal (P) = Rs. 1350
- Time (T) = 3 years
- Difference between two simple interests (SI1 - SI2) = Rs. 40.5

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest (in percentage)
- T = Time (in years)

### Step 3: Set up the equations for the two interests
Let R1 and R2 be the two different rates of interest. Then the two simple interests can be expressed as:
- \( SI1 = \frac{1350 \times R1 \times 3}{100} \)
- \( SI2 = \frac{1350 \times R2 \times 3}{100} \)

### Step 4: Write the equation for the difference in simple interests
According to the problem:
\[ SI1 - SI2 = 40.5 \]
Substituting the expressions for SI1 and SI2:
\[ \frac{1350 \times R1 \times 3}{100} - \frac{1350 \times R2 \times 3}{100} = 40.5 \]

### Step 5: Factor out the common terms
Factoring out the common terms:
\[ \frac{1350 \times 3}{100} (R1 - R2) = 40.5 \]

### Step 6: Simplify the equation
Now, simplify the left side:
\[ \frac{4050}{100} (R1 - R2) = 40.5 \]
This simplifies to:
\[ 40.5 (R1 - R2) = 40.5 \]

### Step 7: Divide both sides by 40.5
Dividing both sides by 40.5 gives:
\[ R1 - R2 = 1 \]

### Step 8: Conclusion
Thus, the difference in the rates of interest (R1 - R2) is:
\[ \boxed{1\%} \]