The simple interest on Rs. 1820 from March 9, 2003 to May 21, 2003 at `7(1)/(2)%` rate will be:

Options

A. Rs. 22.50
B. Rs. 27.30
C. Rs. 28.80
D. Rs. 29

Answer

To find the simple interest on Rs. 1820 from March 9, 2003, to May 21, 2003, at a rate of 7.5%, we will follow these steps:

### Step 1: Calculate the Time Period
First, we need to determine the total number of days from March 9 to May 21.

- **Days remaining in March**: March has 31 days. From March 9 to March 31, there are:
\[ 31 - 9 = 22 \text{ days} \]

- **Days in April**: April has 30 days.
\[ 30 \text{ days} \]

- **Days in May**: From May 1 to May 21, there are:
\[ 21 \text{ days} \]

Now, we add these days together:
\[ 22 \text{ (March)} + 30 \text{ (April)} + 21 \text{ (May)} = 73 \text{ days} \]

### Step 2: Convert Days into Years
Next, we convert the total number of days into years. Since there are 365 days in a year, we calculate:
\[ T = \frac{73}{365} \text{ years} \]

### Step 3: Identify Principal and Rate of Interest
The principal amount (P) is given as Rs. 1820, and the rate of interest (R) is 7.5%. We can express this as a fraction:
\[ R = 7.5\% = \frac{15}{2}\% \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values we have:
\[ SI = \frac{1820 \times \frac{15}{2} \times \frac{73}{365}}{100} \]

### Step 5: Simplify the Expression
Now, we simplify the expression step by step:
1. Calculate \( \frac{15}{2} \times \frac{73}{365} \):
\[ \frac{15 \times 73}{2 \times 365} = \frac{1095}{730} \]

2. Now substitute this back into the SI formula:
\[ SI = \frac{1820 \times \frac{1095}{730}}{100} \]

3. Simplifying further:
- Cancel \( 1820 \) and \( 730 \):
\[ 1820 \div 730 = 2.49 \text{ (approximately)} \]

4. Now calculate:
\[ SI = \frac{2.49 \times 1095}{100} \approx 27.30 \]

### Final Answer
The simple interest is approximately:
\[ \text{SI} \approx Rs. 27.30 \]