The marked price of an article is 10% higher than its cost price. If the shopkeeper allows a discount of 10% on the marked price, what happens to the seller with respect to profit or loss on the cost price?

Introduction / Context:
This question examines a basic profit and loss scenario involving marked price, cost price and discount. It shows that even when a shopkeeper increases the marked price and then gives a discount, the final effect can still be a small loss or profit. This is a classic example to test whether students can correctly handle successive percentage changes on different bases.

Given Data / Assumptions:

• Marked price (MP) is 10% higher than cost price (CP).
• Discount of 10% is allowed on the marked price.
• We must determine whether there is profit, loss or no change, and by what percentage on cost price.
• Assume cost price CP = 100 units for simplicity.

Concept / Approach:
First raise the cost price by 10% to get the marked price. Then apply a 10% discount on the marked price to get the actual selling price. Note that both percentages are applied on different bases: one on cost price and the other on marked price. Finally, compare the resulting selling price with the original cost price to find the profit or loss percentage.

Step-by-Step Solution:
Step 1: Let cost price CP = 100.Step 2: Marked price is 10% higher, so MP = 100 + 10% of 100 = 100 + 10 = 110.Step 3: The shopkeeper allows a 10% discount on MP.Step 4: Selling price SP = MP - 10% of MP = 110 - 11 = 99.Step 5: Compare SP with CP. We have CP = 100 and SP = 99.Step 6: Loss = CP - SP = 100 - 99 = 1.Step 7: Loss percentage on cost price = (Loss / CP) * 100 = (1 / 100) * 100 = 1%.Step 8: Therefore the seller incurs a 1% loss.

Verification / Alternative check:
We can also think in terms of multipliers. Increasing by 10% means multiplying by 1.10. Giving a 10% discount means multiplying by 0.90. So effective factor applied on cost price is 1.10 * 0.90 = 0.99. This means the selling price is 99% of the cost price. Since 99% is 1% less than 100%, this again confirms a 1% loss. This multiplier perspective often simplifies repeated percentage calculations.

Why Other Options Are Wrong:
Option A (bears no gain, no loss) is wrong because SP is slightly below CP. Option B (gains) is incorrect since CP exceeds SP. Option D (None of these) is not right because one of the specific statements, namely a 1% loss, exactly matches the result. Only option C correctly states that the seller loses 1% on the cost price.

Common Pitfalls:
Students sometimes wrongly assume that a 10% increase followed by a 10% decrease will cancel out, leading to no gain or loss. This only happens if the percentage changes are applied on the same base, which is not the case here. Another mistake is to apply both percentages on the cost price instead of on cost price and marked price separately. Remember that discount is always calculated on the marked price, not on the cost price.

Final Answer:
In this transaction, the seller loses 1% on the cost price.