Goods were bought for Rs. 600 and sold the same day for Rs. 650.25 at a credit of 9 months, and still there was a 2% gain. Find the annual rate percent used in discounting.

Introduction / Context: The selling price is on credit; the present worth (cash equivalent) must be computed via true discount so that the net gain relative to cost is 2%. From this, we deduce the annual rate.

Given Data / Assumptions:

• Cost = 600
• Credit price (face value) = 650.25
• Time = 9 months = 0.75 years
• Net gain = 2% → Present worth PW = 600 * 1.02 = 612
• Discounting by true discount (present worth P = F / (1 + r * t))

Concept / Approach: Set PW = F / (1 + r * t) and solve for r, since PW must equal the effective cash value that yields 2% gain over cost.

Step-by-Step Solution: PW = 612 = 650.25 / (1 + r * 0.75). 1 + 0.75 r = 650.25 / 612 = 1.0625. 0.75 r = 0.0625 → r = 0.083333... = 8 1/3% p.a.

Verification / Alternative check: With r = 8 1/3%, present worth is exactly 612. Thus profit = 612 − 600 = 12, i.e., 2% of 600, confirming the calculation.

Why Other Options Are Wrong: 6 1/3% and 7% under-discount the credit price; 9% and 8% over/under shoot the exact present worth condition.

Common Pitfalls: Using banker’s discount instead of TD; not converting months to years; or equating profit to (credit − cost) without discounting.

Final Answer: 8 1/3%