A bill for Rs 6000 is drawn on 14 July at 5 months' term. It is discounted on 5 October at 10% per annum simple interest. Find the net amount that the holder of the bill receives (in rupees).

Introduction / Context:
This question tests understanding of banker's discount in practical date based situations. A bill is drawn with a certain term in months, and then discounted at the bank before its due date. We must carefully determine the remaining time between the date of discount and the legally due date of the bill, including days of grace, and then apply simple interest on the face value to find the banker's discount. Subtracting this discount from the face value gives the net amount received by the holder, also called the proceeds.

Given Data / Assumptions:
- Face value of the bill F = Rs 6000
- Date of drawing the bill = 14 July
- Term of the bill = 5 months
- Date of discount = 5 October
- Rate of simple interest r = 10 percent per annum
- We assume standard practice of adding 3 days of grace to the due date when computing time for discount.

Concept / Approach:
The nominal due date of the bill is obtained by adding the term of 5 months to the date of drawing. Legal due date is three days after the nominal due date. The time for which the bank charges interest is the interval from the date of discount to the legal due date. The banker's discount BD is then BD = F × r × t / 100, where t is measured in years. The proceeds or net amount received by the holder is face value minus banker's discount.

Step-by-Step Solution:
Step 1: Add 5 months to 14 July to get the nominal due date: 14 December.Step 2: Add 3 days of grace to find the legal due date: 17 December.Step 3: Count the number of days from 5 October to 17 December: from 5 October to 31 October is 26 days, plus 30 days in November, plus 17 days in December, for a total of 26 + 30 + 17 = 73 days.Step 4: Convert 73 days to years using 365 days in a year: t = 73 / 365 = 0.2 year.Step 5: Compute banker's discount BD = F × r × t / 100 = 6000 × 10 × 0.2 / 100 = 6000 × 2 / 100 = Rs 120.Step 6: Proceeds or net amount received by the holder = F − BD = 6000 − 120 = Rs 5880.

Verification / Alternative check:
We can confirm that the time fraction is exactly 0.2 year because 73 ÷ 365 equals 0.2. At 10 percent per annum, interest for one year on Rs 6000 would be Rs 600. For one fifth of a year, the interest is one fifth of Rs 600, which is Rs 120. This matches the computed banker's discount. Subtracting 120 from the face value 6000 yields Rs 5880 consistently as the proceeds.

Why Other Options Are Wrong:
An amount like 6580 would exceed the face value, which is impossible as the bank always deducts a discount, not adds to the amount. Values like 4390 or 5350 imply a discount much larger than Rs 120 and are not consistent with a modest 10 percent annual rate for only 73 days. The option 5700 also does not match the exact simple interest calculation. Only Rs 5880 fits the correct banker's discount computation.

Common Pitfalls:
Many students forget to include 3 days of grace in the time computation or mistakenly count the term from the date of discount instead of from the date of drawing. Another error is to treat 73 days as 73 months or to divide by 360 instead of 365, leading to slightly different results. Being systematic about dates and always converting the exact number of days to a year fraction avoids these mistakes.

Final Answer:
The holder of the bill receives a net amount of 5880 rupees.