By selling a T-shirt on marked price of 650, a shopkeeper gains 25%. During a clearance sale, the shopkeeper allows a discount of 20% on the marked price. What is the overall profit/loss?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → No profit, no loss
Profit or loss is judged by comparing the selling price with the cost price. The 25% gain at the marked price gives the cost price; the 20% discount gives the sale price.
Selling at the marked price gives a 25% gain, so cost price \(\displaystyle =\frac{650}{1.25}=520\)
Price in the sale, 20% below the marked price \(=650\times0.8=520\)
Sale price = cost price, so there is no profit and no loss
Shortcut: The two changes can be combined without using the price at all.
Marked price \(=1.25\times\) cost price
Sale price \(=0.8\times\) marked price \(=0.8\times1.25\times\) cost price
\(0.8\times1.25=1\), so the sale price equals the cost price