Dating a discounted bill with grace: A bill for ₹17850 is nominally due on May 21, 1991. The holder received ₹357 less than the bill amount by discounting it at 5% simple interest. On which date was it discounted? (Assume the usual 3 days of grace on the bill.)

Introduction / Context: To find the discounting date, first compute the time interval t for which the bill was discounted using banker’s discount BD = Face * r * t. Many bill problems include 3 days of grace, meaning the legal due date is 3 days after the nominal date; this affects the backward count when converting time to a calendar date.

Given Data / Assumptions:

• Face value F = ₹17850.
• Discount rate r = 5% p.a. (simple).
• Banker’s discount BD = ₹357.
• Assume standard 3 grace days beyond the nominal due date.

Concept / Approach: Compute t from BD = F * r * t. Convert t years to days. Add grace (for due date) and count back to the discounting date from the legal due date.

Step-by-Step Solution:

Verification / Alternative check: Counting back 146 days from May 24, 1991 to Dec 29, 1990 matches standard solutions; without grace, you would get Dec 26, 1990.

Why Other Options Are Wrong: Dates in 1989 or 1995 are inconsistent; Dec 19, 1990/Dec 26, 1990 correspond to different grace assumptions.

Common Pitfalls: Forgetting the 3 days of grace or mixing 360-day and 365-day conventions without instruction.

Final Answer: Dec 29, 1990