Discount with profit: After allowing a 16% discount, a shopkeeper still makes a 5% gain. By what percentage is the marked price above the cost price?

Introduction / Context:The question connects discount on marked price (MP) with gain on cost price (CP). Converting both to a single equation allows solving for MP/CP and hence the percentage markup over cost.

Given Data / Assumptions:

• Discount = 16% on MP ⇒ SP = 0.84 * MP.
• Gain = 5% on CP ⇒ SP = 1.05 * CP.

Concept / Approach:Equate the two expressions for SP to relate MP and CP, then convert the ratio to a percentage increase of MP over CP: (MP − CP)/CP * 100%.

Step-by-Step Solution:

Verification / Alternative check:Assume CP = 100; then SP = 105. Since SP = 0.84*MP, MP = 105/0.84 = 125 = 25% above 100.

Why Other Options Are Wrong:15%, 18%, 21% do not satisfy 0.84*MP = 1.05*CP. Only 25% yields equality.

Common Pitfalls:Adding or subtracting percentages directly rather than forming and equating the correct expressions.

Final Answer:25%