Profit and Loss – Marked price, discount, and realized profit: Kabir buys an article at a 25% discount on its marked price and sells it for Rs 660, making a 10% profit on his cost. What is the marked price?

Introduction / Context:
Marked price (MP), discount, and realized selling price (SP) are related through cost price (CP). A discount reduces MP to CP, and the final SP gives a margin over CP. Here both the discount and the realized profit are given, which uniquely determine MP.

Given Data / Assumptions:

• Discount = 25% on MP ⇒ CP = 0.75 * MP
• SP = Rs 660
• Profit on CP = 10% ⇒ SP = 1.10 * CP

Concept / Approach:
From SP = 1.10 * CP, compute CP. Then back out MP using CP = 0.75 * MP.

Step-by-Step Solution:
CP = SP / 1.10 = 660 / 1.10 = Rs 6000.75 * MP = 600 ⇒ MP = 600 / 0.75 = Rs 800Wait: 600 / 0.75 = 800; but cross-check with discount-to-SP chain: SP = 0.75 * MP * 1.10 = 0.825 * MP ⇒ MP = 660 / 0.825 = 800Correct marked price = Rs 800? Recheck initial assumption: Discount of 25% means CP to Kabir is 75% of MP; selling at 10% profit on CP gives SP = 1.10 * CP = 1.10 * 0.75 * MP = 0.825 MP ⇒ MP = 660 / 0.825 = 800

Verification / Alternative check:
Using MP = 800: discounted purchase price = 600; selling at 10% profit gives SP = 660, consistent.

Why Other Options Are Wrong:
880, 700, 600, and 685 do not satisfy SP = 0.825 * MP relation when SP = 660.

Common Pitfalls:
Confusing “25% discount on MP” with “25% profit.” They apply on different bases.

Final Answer:
Rs 800