Marked price, discount, and gain: The cost price (CP) of an article is 64% of its marked price (MP). If a discount of 12% is allowed on the MP, what is the gain percentage on CP?

Introduction / Context:
This problem combines two percentage chains: cost to marked price, and marked price to selling price via discount. The final aim is to compute the gain percentage relative to the cost price after discounting from the marked price.

Given Data / Assumptions:

• CP = 64% of MP ⇒ CP = 0.64 * MP.
• Discount = 12% on MP ⇒ SP = 0.88 * MP.
• Gain % = [(SP − CP)/CP] * 100.

Concept / Approach:
Use a symbolic MP (e.g., MP = M). Express CP and SP in terms of M, then compute gain% with CP as the base. The M cancels out, leaving a clean percentage result independent of actual prices.

Step-by-Step Solution:

Verification / Alternative check:
Pick a concrete MP, say 100. Then CP = 64 and SP = 88, so gain = 24 on cost 64 ⇒ 24/64 = 0.375 = 37.5%. Matches the symbolic result.

Why Other Options Are Wrong:

• 48%, 50.5%, 52%, 35%: These values result from mixing bases or subtracting percentages instead of applying them to MP and CP correctly.

Common Pitfalls:
Using discount on CP or computing profit over MP. Always maintain the correct bases: discount on MP; profit on CP.

Final Answer:
37.5%