A shopkeeper wants to allow a 20% cash discount yet still earn a 20% profit on cost. What should be the marked price of an item whose cost price is ₹180?

Introduction / Context:
To meet a profit target after granting a discount on the marked price, we first find the required selling price from the profit requirement, then work backward to the marked price using the discount percentage.

Given Data / Assumptions:

• Cost price (CP) = ₹180.
• Desired profit = 20% on CP.
• Cash discount = 20% on marked price (MP).

Concept / Approach:
Required SP = 1.20 * CP. Also, SP = (1 − 0.20) * MP = 0.80 * MP. Equate these to solve for MP.

Step-by-Step Solution:
Required SP = 1.20 * 180 = ₹2160.80 * MP = 216 ⇒ MP = 216 / 0.80 = ₹270

Verification / Alternative check:
Applying 20% off on ₹270 gives ₹216; profit over ₹180 is ₹36 → 20%.

Why Other Options Are Wrong:
₹240, ₹245, ₹260: After 20% off, these do not yield a selling price of ₹216.

Common Pitfalls:
Adding discounts and profits directly; using CP as the discount base by mistake rather than the marked price.

Final Answer:
₹ 270