Profit without discount vs with discount: The marked price of a radio is ₹480. With a 10% discount, the shopkeeper still gains 8%. If no discount were given, what would the profit percentage be?

Introduction / Context: First recover the cost price from the discounted sale that yields an 8% gain. Then compare the full MRP to that cost to compute the hypothetical profit with no discount. This keeps percentage bases consistent and avoids shortcuts that misapply percentages.

Given Data / Assumptions:

• MRP M = ₹480.
• Discount = 10% ⇒ SP(discounted) = 0.9M = ₹432.
• Gain at discounted sale = 8% ⇒ C = 432 / 1.08.

Concept / Approach: Compute cost from the actual sale, then compute profit% for a sale at M: Profit% = [(M − C)/C] * 100.

Step-by-Step Solution:

Verification / Alternative check: At discount: profit = 432 − 400 = 32 ⇒ 32/400 = 8%. At MRP: 80/400 = 20%, as found.

Why Other Options Are Wrong: 18%, 18.5%, 20.5%, 22% do not match the exact computation with the verified cost.

Common Pitfalls: Using 8% directly on the MRP or assuming linearity between discount and profit without referencing cost.

Final Answer: 20 %