Credit sale with true-discount valuation: A man purchased a cow for Rs. 300 and sold it the same day for Rs. 360, allowing the buyer a credit of 2 years. If the simple-interest rate is 7 1/2% per annum, what is his gain percentage?

Introduction / Context:
When goods are sold on credit, the quoted selling price is a future amount. To assess real profit, convert that future amount to present worth using the given simple-interest rate, and compare with the cash cost price. The percentage gain = (Profit / Cost) * 100.

Given Data / Assumptions:

• Cost price (cash) = 300.
• Selling price quoted for payment in 2 years = 360.
• Rate r = 7.5% per annum simple; present worth PW = A / (1 + r * t).

Concept / Approach:
Present worth of SP is PW = 360 / (1 + 0.075 * 2) = 360 / 1.15. Profit in present terms = PW − 300. Profit % = [(PW − 300) / 300] * 100.

Step-by-Step Solution:
PW = 360 / 1.15 = 313.0435…Profit = 313.0435 − 300 = 13.0435.Profit % = 13.0435 / 300 * 100 ≈ 4.3478% ≈ 4 1/2%.

Verification / Alternative check:
Accrue the cost for two years at 7.5%: Future value of cost = 300 * (1 + 0.075 * 2) = 345. Compare future selling price 360 vs 345; the gain at that future moment is 15 on a future-cost base 345, which still corresponds to approximately 4.35% on the original cost when brought back to present terms.

Why Other Options Are Wrong:

• 53/7% (~7.57%), 6%, and 5% do not match the exact present-worth calculation.

Common Pitfalls:

• Treating 360 as cash received today and computing (360 − 300)/300.
• Using compound instead of simple interest for discounting.

Final Answer:
41/2%