Required markup with a fixed discount: A tradesman allows a 15% discount on the marked price. By what percentage above the cost price must he mark the goods to gain 19% after giving this discount?

Introduction / Context:
We need to determine the markup (MP over CP) when discount is known and desired profit is fixed. The selling price is controlled by both MP and discount, while profit compares SP to CP.

Given Data / Assumptions:

• Discount = 15% ⇒ SP = 0.85 * MP.
• Desired profit = 19% ⇒ SP = 1.19 * CP.

Concept / Approach:
Equate SP expressions: 0.85 * MP = 1.19 * CP. Then compute MP/CP and convert to percent above cost = (MP − CP)/CP * 100%.

Step-by-Step Solution:

Verification / Alternative check:
Let CP = 100 ⇒ MP = 140. After 15% discount SP = 140*0.85 = 119, which is indeed 19% above 100.

Why Other Options Are Wrong:
34%, 25%, 30%, 36% do not satisfy the equality SP = 0.85*MP = 1.19*CP.

Common Pitfalls:
Adding percentages directly instead of forming the equation with multiplicative factors.

Final Answer:
40%