Rs 500 were deposited for 2years in two different banks respectively. If the difference between the simple interest was Rs 2.50, find out the difference in the rate of interest of both banks?

Options

A. `2.5%`
B. `0.23%`
C. `25%`
D. `0.25%`

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 formula for Simple Interest
The formula for Simple Interest is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (initial deposit)
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

### Step 2: Set up the equation for both banks
Let the rate of interest for the first bank be \( R_1 \) and for the second bank be \( R_2 \). The principal amount \( P \) is Rs 500 and the time \( T \) is 2 years.

The Simple Interest for the first bank (SI1) is:
\[ \text{SI}_1 = \frac{500 \times R_1 \times 2}{100} = 10R_1 \]

The Simple Interest for the second bank (SI2) is:
\[ \text{SI}_2 = \frac{500 \times R_2 \times 2}{100} = 10R_2 \]

### Step 3: Write the equation based on the difference in Simple Interest
According to the problem, the difference in Simple Interest between the two banks is Rs 2.50. Therefore, we can write:
\[ \text{SI}_1 - \text{SI}_2 = 2.50 \]
Substituting the values we found:
\[ 10R_1 - 10R_2 = 2.50 \]

### Step 4: Simplify the equation
We can simplify the equation by dividing everything by 10:
\[ R_1 - R_2 = \frac{2.50}{10} \]
\[ R_1 - R_2 = 0.25 \]

### Step 5: Conclusion
The difference in the rate of interest between the two banks is:
\[ R_1 - R_2 = 0.25 \]
To express this as a percentage, we multiply by 100:
\[ \text{Difference in rates} = 0.25 \times 100 = 25\% \]

### Final Answer
The difference in the rate of interest of both banks is **25%**.

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