Marked-up then discounted: determine overall gain or loss An article is marked 40% above cost price and then sold at a 30% discount on the marked price. What is the net percentage gain or loss relative to cost price?

Introduction / Context:
Retail pricing often involves marking up from cost and then discounting for sale. The combined effect is multiplicative, and the outcome could be a gain or a loss depending on the magnitudes of markup and discount.

Given Data / Assumptions:

• Let cost price (CP) = C.
• Marked price (MP) = C * (1 + 0.40) = 1.4C.
• Discount on MP = 30% ⇒ selling price (SP) = MP * 0.70 = 1.4C * 0.70.

Concept / Approach:
Compute SP as a multiple of C, then compare SP to C. Gain/Loss% = (SP − C) / C * 100. If negative, it is a loss.

Step-by-Step Solution:
SP = 1.4C * 0.70 = 0.98C.Gain/Loss% = (0.98C − C) / C * 100 = −0.02 * 100 = −2%.Therefore, there is a 2% loss.

Verification / Alternative check:
Plug a number: If C = 100, MP = 140; 30% off MP gives SP = 98, which is 2 less than cost, confirming a 2% loss.

Why Other Options Are Wrong:
Any gain options contradict SP = 0.98C; larger loss values like 12% do not match the computed product.

Common Pitfalls:
Adding or subtracting percentages directly (e.g., 40 − 30 = 10% gain). This ignores the multiplicative effect and leads to incorrect conclusions.

Final Answer:
2% loss