List price to meet target profit with a discount: A merchant buys a wristwatch for ₹450 and wants a 20% profit after allowing a 10% discount. What should be the list (marked) price?

Introduction / Context:
This is the classic reverse-calculation: compute the necessary SP from CP and desired profit, then back out MP using the given discount. It is identical in structure to similar problems where SP = (1 + profit%) * CP and SP = (1 − discount%) * MP.

Given Data / Assumptions:
CP = ₹450, profit = 20% ⇒ SP = 1.20 * 450 = ₹540; discount = 10% ⇒ SP = 0.90 * MP.

Concept / Approach:
Equate SP = 0.90 * MP = 540 ⇒ solve MP = 540 / 0.90 = 600.

Step-by-Step Solution:

Verification / Alternative check:
Check: 10% off 600 gives 540, which is 20% above 450.

Why Other Options Are Wrong:
650, 700, 550, 620 do not satisfy both the 10% discount and 20% profit conditions simultaneously.

Common Pitfalls:
Applying the 10% discount to CP instead of to MP; mixing up net gain with markup.

Final Answer:
₹ 600