Find discount date from proceeds paid: A banker paid Rs 5767.20 for a bill of Rs 5840, drawn on April 4 at 6 months, at a rate of 7% per annum. On what date was the bill discounted? (Assume 3 days grace.)

Introduction / Context:
Given face value S, proceeds P, and rate r, we can find the banker’s discount BD = S − P and hence the time t between discount date and maturity. Counting back t from the maturity date yields the discount date.

Given Data / Assumptions:

• S = 5840; P = 5767.20 → BD = 72.80.
• r = 7% p.a.; drawn April 4 at 6 months → nominal due Oct 4; +3 days grace → maturity Oct 7.

Concept / Approach:
t = BD / (S * r) (years). Convert to days and count back from Oct 7 to find the calendar date.

Step-by-Step Solution:

Verification / Alternative check:
Recompute BD using 65 days: t ≈ 65/365; BD ≈ 5840 * 0.07 * (65/365) ≈ 72.8 ✔️.

Why Other Options Are Wrong:
Other listed months/dates produce intervals inconsistent with the computed BD at 7%.

Common Pitfalls:
Omitting days of grace; mixing 360 and 365 day bases without checking against BD.

Final Answer:
3rd August