Maximum discount for break-even: A merchant initially marks goods up by 40% above cost. Approximately what maximum percentage discount on the marked price will result in no profit and no loss?

Introduction / Context:
Break-even occurs when SP = CP. Starting from a markup, apply a discount d so that the final selling price equals cost. Solve for d as a fraction of the marked price (MP).

Given Data / Assumptions:

• MP = 1.40 * CP (40% markup).
• We need SP = CP after discount d% on MP.

Concept / Approach:
SP = MP * (1 − d). For break-even: MP * (1 − d) = CP ⇒ (1 − d) = CP / MP = 1 / 1.40.

Step-by-Step Solution:

Verification / Alternative check:
Let CP = 100 ⇒ MP = 140. With a 28.57% discount, SP ≈ 140*0.7143 = 100, as required.

Why Other Options Are Wrong:
33.5% overshoots and causes a loss; 60% is far too high; “No discount” ignores the markup; 40% would lead to a loss.

Common Pitfalls:
Confusing percentage of cost with percentage of marked price when discounting.

Final Answer:
28.5%