Cash sale after discount on marked-up goods: A seller marks goods 30% above cost and allows a 15% cash discount. What is his percentage profit on a cash sale?

Introduction / Context:
Profit under successive mark-up and discount is multiplicative in factors: mark up by 30% (factor 1.30), then discount by 15% (factor 0.85). The net selling price relative to cost gives the overall profit percentage for the cash transaction.

Given Data / Assumptions:

• Cost = C.
• Marked price M = 1.30C.
• Cash discount = 15% ⇒ Selling price S = 0.85M.

Concept / Approach:
Combine the multiplicative factors: S = 0.85 * 1.30 * C = 1.105C. Profit% = (S − C)/C * 100 = (1.105 − 1) * 100.

Step-by-Step Solution:

Verification / Alternative check:
With C = 100, M = 130, cash S = 110.5, profit = 10.5, i.e., 10.5%.

Why Other Options Are Wrong:
15% ignores the discount; 9% or 8.5% understate the net factor; 12% overstates it.

Common Pitfalls:
Adding or subtracting percentages arithmetically; always multiply factors for successive mark-ups/discounts.

Final Answer:
10.5%