The simple interest on Rs. 1200 from 4th January, 1984 to 29th May, 1985 at 3% per annum in Rupees is

Options

A. `14.40`
B. `50.40`
C. `15.40`
D. `51.40`

Answer

To calculate the simple interest on Rs. 1200 from 4th January 1984 to 29th May 1985 at a rate of 3% per annum, we will follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- **Principal (P)** = Rs. 1200
- **Rate (R)** = 3% per annum

### Step 2: Calculate the Time Period (T)
We need to calculate the time period from 4th January 1984 to 29th May 1985.

#### Part 1: Calculate Days in 1984
- From 4th January 1984 to 31st December 1984:
- Total days in 1984 (leap year) = 366 days
- Days from 1st January to 3rd January = 3 days
- Days from 4th January to 31st December = 366 - 3 = 363 days

#### Part 2: Calculate Days in 1985
- From 1st January 1985 to 29th May 1985:
- January: 31 days
- February: 28 days
- March: 31 days
- April: 30 days
- May: 29 days (up to 29th)

Total days in 1985 = 31 + 28 + 31 + 30 + 29 = 149 days

#### Total Days from 4th January 1984 to 29th May 1985
- Total days = Days in 1984 + Days in 1985 = 363 + 149 = 512 days

### Step 3: Convert Days to Years
To convert days into years:
\[ T = \frac{512 \text{ days}}{365 \text{ days/year}} \approx 1.40 \text{ years} \]

### Step 4: Calculate Simple Interest (SI)
Using the formula for simple interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{1200 \times 3 \times 1.40}{100} \]
Calculating:
\[ SI = \frac{1200 \times 3 \times 1.40}{100} = \frac{5040}{100} = 50.4 \text{ Rupees} \]

### Final Answer
The simple interest on Rs. 1200 from 4th January 1984 to 29th May 1985 at 3% per annum is **Rs. 50.4**.

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