The holder of a bill for Rs. 17850 nominally due on 21st May, 1991 received Rs. 357 less than the amount of the bill by having it discounted at `5%`. When was it discounted ?

Options

A. December 29, 1990
B. December 30,1989
C. December 19, 1990
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Given Information
- The nominal amount of the bill = Rs. 17850
- The amount received after discount = Rs. 17850 - Rs. 357 = Rs. 17493
- The rate of discount = 5%
- Due date of the bill = 21st May 1991

### Step 2: Calculate the Simple Interest (SI)
The difference between the nominal amount and the amount received is the simple interest (SI) on the bill.

\[ SI = 357 \text{ (as given)} \]

### Step 3: Use the Simple Interest Formula
The formula for simple interest is:

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

Where:
- \( P \) = Principal amount (Rs. 17850)
- \( R \) = Rate of interest (5%)
- \( T \) = Time in years

Rearranging the formula to find time \( T \):

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

### Step 4: Substitute the Values
Substituting the known values into the equation:

\[ T = \frac{357 \times 100}{17850 \times 5} \]

### Step 5: Calculate \( T \)
Calculating the above expression:

\[ T = \frac{35700}{89250} = \frac{2}{5} \text{ years} \]

### Step 6: Convert Time to Days
To convert \( \frac{2}{5} \) years into days, we multiply by 365 days:

\[ T = \frac{2}{5} \times 365 = 146 \text{ days} \]

### Step 7: Determine the Discount Date
Since the bill is due on 21st May 1991, we need to go back 146 days to find the discount date.

### Step 8: Count Back 146 Days from 21st May 1991
- Days in May before the 21st: 20 days (from 1st to 20th May)
- Days in April: 30 days
- Days in March: 31 days
- Days in February: 28 days (1991 is not a leap year)
- Days in January: 31 days

Now, we add these days until we reach 146 days:

1. May: 20 days
2. April: 30 days (Total = 20 + 30 = 50 days)
3. March: 31 days (Total = 50 + 31 = 81 days)
4. February: 28 days (Total = 81 + 28 = 109 days)
5. January: 31 days (Total = 109 + 31 = 140 days)

Now we need 6 more days to reach 146 days, which takes us into December.

### Step 9: Final Calculation
- 6 days back from 31st December leads us to **25th December 1990**.

### Conclusion
The bill was discounted on **25th December 1990**.

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