12000 is lent at rate of 15% simple interest on 29 January 1987 and a certain amount is returned on 23 June 1987. If both dates are counted then what is the simple interest ?

Options

A. Rs 620
B. Rs 820
C. Rs 680
D. Rs 720

Answer

To solve the question, we need to calculate the simple interest on a principal amount of ₹12,000 at a rate of 15% for a specific time period. Here’s the step-by-step solution:

### Step 1: Identify the Principal, Rate, and Time
- **Principal (P)** = ₹12,000
- **Rate (R)** = 15% per annum
- **Time (T)** = From 29 January 1987 to 23 June 1987

### Step 2: Calculate the Time in Days
To find the time in days, we need to count the number of days from 29 January 1987 to 23 June 1987.

- January: 2 days (30th and 31st)
- February: 28 days (1987 is not a leap year)
- March: 31 days
- April: 30 days
- May: 31 days
- June: 23 days

Now, add these days together:
\[ \text{Total Days} = 2 + 28 + 31 + 30 + 31 + 23 = 145 \text{ days} \]

### Step 3: Convert Days to Years
Since the interest rate is per annum, we need to convert the time from days to years:
\[ T = \frac{145}{365} \text{ years} \]

### 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:
\[ SI = \frac{12000 \times 15 \times \frac{145}{365}}{100} \]

### Step 5: Calculate the Simple Interest
Now, let's calculate the simple interest:
1. Calculate \( \frac{145}{365} \):
\[ \frac{145}{365} \approx 0.39726 \]
2. Substitute this back into the SI formula:
\[ SI = \frac{12000 \times 15 \times 0.39726}{100} \]
3. Calculate \( 12000 \times 15 = 180000 \):
\[ SI = \frac{180000 \times 0.39726}{100} \approx 716.88 \]
4. Rounding off, we get:
\[ SI \approx 717 \]

### Final Answer
The simple interest is approximately ₹717.

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