A shop offers a 60% discount on the marked price of an item, and after this discount the selling price becomes equal to the cost price. What was the percentage markup of the marked price over the cost price?

Introduction / Context:
This question reverses the usual selling price calculation and asks about markup. The shopkeeper sets a marked price above the cost price and then gives a heavy discount. The special situation here is that, after a 60% discount, the final selling price exactly equals the cost price. We must determine how much higher the marked price was compared to the cost price. This is a straightforward percentage reasoning problem.

Given Data / Assumptions:

• Let cost price be C.
• Marked price is unknown, call it M.
• Discount given on M is 60%.
• After discount, selling price equals cost price C.
• We need the percentage markup, that is (M - C) as a percentage of C.

Concept / Approach:
If the discount is 60%, then:

• Selling price SP = M * (1 - 60/100) = 0.4M.
• Given SP = C.
• Therefore 0.4M = C, so M = C / 0.4 = 2.5C.
• Markup percent = ((M - C) / C) * 100.
• Since M = 2.5C, markup = 1.5C, so markup percent = 150%.

Step-by-Step Solution:
Let cost price be C. Let marked price be M. A 60% discount on M means the customer pays 40% of M. Therefore selling price SP = 0.4M. Given that after discount SP = C. So 0.4M = C. M = C / 0.4 = 2.5C. Markup = M - C = 2.5C - C = 1.5C. Markup percentage = (1.5C / C) * 100 = 150%.

Verification / Alternative check:
Assume a convenient cost price, for example C = 100 rupees.

• Then marked price M = 2.5 * 100 = 250.
• Discount 60% on 250 gives discount = 150 rupees.
• Selling price = 250 - 150 = 100.
• The selling price equals the cost price, as required.
• Markup from 100 to 250 is 150%, which agrees with our calculation.

Why Other Options Are Wrong:
Markup of 100% would mean marked price is double the cost price. After 60% discount, the selling price would be 40% of 200, which is 80, not equal to the cost price. Markups of 250%, 40%, or 200% also lead to different selling prices after a 60% discount and do not match the condition that the selling price equals cost price. Only a 150% markup fits the given discount relation.

Common Pitfalls:
Learners sometimes treat discount on cost price instead of marked price or mix up markup percentage with discount percentage. Another frequent mistake is not converting the verbal relation "selling price becomes equal to cost price" into a simple equation. Always express selling price in terms of marked price and discount, then equate it to cost price when such conditions are mentioned.

Final Answer:
The marked price was increased by 150% over the cost price.