A bill for Rs. 5656 is drawn on july 14 at 5 months. It is discounted on Oct. 5th at `5%`-----
Banker's discount

Options

A. Rs. 56.56
B. Rs.56
C. Rs.56.50
D. None of these

Answer

To solve the problem of finding the Banker's Discount for a bill of Rs. 5656 drawn on July 14 for 5 months and discounted on October 5 at a rate of 5%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amount and Dates**:
- Amount (A) = Rs. 5656
- Date of drawing the bill = July 14
- Time for which the bill is drawn = 5 months
- Date of discounting the bill = October 5

2. **Calculate the Nominal Due Date**:
- The nominal due date is 5 months from the date of drawing.
- July 14 + 5 months = December 14.

3. **Calculate the Legally Due Date**:
- The legally due date is typically a few days after the nominal due date.
- In this case, it is December 17.

4. **Calculate the Unexpired Time**:
- The unexpired time is the time remaining from the discounting date (October 5) to the legally due date (December 17).
- From October 5 to October 31 = 26 days (October has 31 days)
- November = 30 days
- From December 1 to December 17 = 17 days
- Total unexpired time = 26 + 30 + 17 = 73 days.

5. **Convert Unexpired Time to Years**:
- Since there are 365 days in a year, we convert 73 days into years:
- Unexpired time in years = 73/365 = 1/5 years (approximately).

6. **Calculate the Banker's Discount**:
- The formula for Banker's Discount (BD) is:
\[ BD = \text{Amount} \times \text{Rate} \times \text{Time} \]
- Here, Rate = 5% = 5/100 = 0.05.
- Substitute the values into the formula:
\[ BD = 5656 \times 0.05 \times \frac{1}{5} \]
- Simplifying this:
\[ BD = 5656 \times 0.05 \times 0.2 = 5656 \times 0.01 = 56.56 \]

7. **Final Answer**:
- The Banker's Discount is Rs. 56.56.