Find the marked price: An article costs ₹450. A shopkeeper allows a 10% discount to customers and still gains 20%. What is the marked price?

Introduction / Context:
Given CP and both discount and profit requirements, we compute the necessary marked price (MP). The selling price must satisfy both relations simultaneously: SP = 0.90*MP and SP = 1.20*CP.

Given Data / Assumptions:

• CP = ₹450
• Discount = 10% ⇒ SP = 0.90 * MP
• Profit = 20% ⇒ SP = 1.20 * CP = ₹540

Concept / Approach:
Equate SP from both expressions and solve for MP: 0.90*MP = 540 ⇒ MP = 600.

Step-by-Step Solution:

Verification / Alternative check:
With MP = 600, a 10% discount gives SP = 540, which is 20% above 450.

Why Other Options Are Wrong:
₹540 is the SP, not MP; ₹660, ₹580, ₹620 do not satisfy 0.90*MP = 540.

Common Pitfalls:
Using 10% of CP instead of 10% of MP for discounting.

Final Answer:
₹ 600