Find the simple interest on Rs. 500 at 6% per annum from May 3rd to July 15th in the same year.

Answer

To find the simple interest on Rs. 500 at 6% per annum from May 3rd to July 15th in the same year, we will follow these steps:

### Step 1: Calculate the number of days from May 3rd to July 15th.

1. **Days in May**:
- May has 31 days.
- From May 3rd to May 31st, the number of days is \(31 - 3 = 28\) days.

2. **Days in June**:
- June has 30 days, so there are 30 days in June.

3. **Days in July**:
- From July 1st to July 15th, the number of days is 15 days.

4. **Total Days**:
- Total days from May 3rd to July 15th is \(28 + 30 + 15 = 73\) days.

### Step 2: Use the Simple Interest formula.

The formula for Simple Interest (SI) is given by:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \(P\) = Principal amount (Rs. 500)
- \(R\) = Rate of interest (6% per annum)
- \(T\) = Time in years

### Step 3: Convert the time from days to years.

Since the time \(T\) is in days, we need to convert it to years:

\[ T = \frac{73 \text{ days}}{365 \text{ days/year}} = \frac{73}{365} \text{ years} \]

### Step 4: Substitute the values into the formula.

Now we can substitute the values into the Simple Interest formula:

\[ SI = \frac{500 \times 6 \times \frac{73}{365}}{100} \]

### Step 5: Simplify the expression.

1. Calculate the numerator:
- \(500 \times 6 = 3000\)
- \(3000 \times 73 = 219000\)

2. The expression now looks like:
- \[ SI = \frac{219000}{36500} \]

3. Simplifying gives:
- \[ SI = \frac{219000}{36500} = 6 \]

### Final Answer:

The simple interest is Rs. 6.

---