Marked-up goods and discount: A merchant marks goods 20% above cost and then allows a 15% discount on the marked price. What is his overall gain percentage?

Introduction / Context:This is a classic chain percentage problem linking cost price (CP), marked price (MP), discount, and selling price (SP). We compute SP in terms of CP and then convert the difference to a gain percentage.

Given Data / Assumptions:

• MP = CP * (1 + 20%) = 1.20 * CP
• Discount on MP = 15% ⇒ SP = MP * 0.85

Concept / Approach:SP = CP * 1.20 * 0.85. Then gain% = [(SP − CP)/CP] * 100%.

Step-by-Step Solution:SP = CP * 1.20 * 0.85 = CP * 1.02Gain = SP − CP = 0.02 * CPGain% = (0.02 * CP)/CP * 100% = 2%

Verification / Alternative check:Take CP = ₹100. MP = ₹120. After 15% discount, SP = ₹102. Gain = ₹2 ⇒ 2%.

Why Other Options Are Wrong:1% or 5% and 10% do not match the multiplicative effect; 15% confuses the discount with profit.

Common Pitfalls:Subtracting percentages (20% − 15% = 5%) to infer profit; the base of 15% is MP, not CP.

Final Answer:2%