The difference between the simple interset received from two diferent sources on Rs 1500 for 3 years is Rs 13.50. The difference between their rates of interset is :

Options

A. `0.1%`
B. `0.2 %`
C. `0.3%`
D. `0.4%`

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 Problem
We are given:
- Principal (P) = Rs. 1500
- Time (T) = 3 years
- Difference in Simple Interest (SI) = Rs. 13.50

We need to find the difference between the rates of interest (R1 and R2).

### Step 2: Calculate the Difference in SI per Year
Since the total difference in SI over 3 years is Rs. 13.50, we can find the difference in SI for 1 year.

\[ \text{Difference in SI per year} = \frac{\text{Total Difference in SI}}{\text{Number of Years}} = \frac{13.50}{3} = Rs. 4.50 \]

### Step 3: Use the SI Formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest
- T = Time in years

Let R1 and R2 be the rates of interest for the two sources. The difference in SI for one year can be expressed as:
\[ SI_1 - SI_2 = \frac{P \times R1 \times 1}{100} - \frac{P \times R2 \times 1}{100} = \frac{P \times (R1 - R2)}{100} \]

### Step 4: Set Up the Equation
From Step 2, we know that:
\[ \frac{1500 \times (R1 - R2)}{100} = 4.50 \]

### Step 5: Solve for the Difference in Rates
Now, we can solve for \( R1 - R2 \):
\[ 1500 \times (R1 - R2) = 4.50 \times 100 \]
\[ 1500 \times (R1 - R2) = 450 \]
\[ R1 - R2 = \frac{450}{1500} = 0.30 \]

### Step 6: Convert to Percentage
Since the difference in rates is expressed in percentage:
\[ R1 - R2 = 0.30 \times 100 = 30\% \]

### Final Answer
The difference between their rates of interest is **30%**.

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