Find the discounting date from proceeds: A banker pays ₹5767.50 for a bill of ₹5840 drawn on April 4 at 6 months. At 7% per annum simple interest, on which date was the bill discounted?

Introduction / Context:
Discounting a bill means the banker deducts interest (banker’s discount) from the face value for the time remaining until the due date. From the proceeds (cash paid), we can infer the time between discount date and due date and hence the calendar date of discount.

Given Data / Assumptions:

• Face value A = ₹5840
• Proceeds (cash paid) = ₹5767.50 ⇒ BD = A − Proceeds = ₹72.50
• Rate r = 7% p.a.
• Term = 6 months from April 4; customary 3 days of grace ⇒ due about October 7

Concept / Approach:
Banker’s Discount: BD = A * r * t, for t (in years) from discount date to due date. Solve for t, convert to days, then back-date from October 7 to find the discount date.

Step-by-Step Solution:

Verification / Alternative check:
Using 365-day basis gives near-exact 65 days; counting back from Oct 7 lands on about Aug 3. Small convention differences (360-day basis) shift by < 1 day, still pointing to the first days of August.

Why Other Options Are Wrong:
Aug 4 or September dates imply fewer/more days than supported by BD = ₹72.50 at 7% and are inconsistent with the computed interval.

Common Pitfalls:
Omitting days of grace when used in such problems, forgetting to compute t from BD on the face value, or mixing up due date vs. term date.

Final Answer:
3rd Aug.