Percentage · increase then decrease

Question

At a shop in Toa Payoh, the price of a pair of sports shoes was first increased by 20%. Later, during a sale, the new price was decreased by 25%. The sale price was $72. What was the original price of the shoes?

Practice: 3 similar questions

1. The price of a T-shirt was first increased by 20% and later decreased by 10%. Its final selling price was $54. What was its original price?
   Answer

   50 $ — The original price is 100%. After a 20% increase, it becomes 120%. After a 10% decrease, 90% × 120% = 108% of the original price remains. 108% corresponds to $54, so 1% corresponds to $0.50 and 100% corresponds to $50.

2. Raju's number of cards first increased by 30%. Later, he gave away 20% of the cards he then had and had 208 cards left. How many cards did Raju have at first?
   Answer

   200 张 — The original number of cards is 100%. After a 30% increase, it becomes 130%. After giving away 20%, 80% × 130% = 104% of the original number remains. 104% corresponds to 208 cards, so 1% corresponds to 2 cards and 100% corresponds to 200 cards.

3. The price of a bicycle was first increased by 25%. Later, during a sale, it was decreased by 24%. The sale price was $760. What was the original price of the bicycle?
   Answer

   800 $ — The original price is 100%. After a 25% increase, it becomes 125%. After a 24% decrease, 76% × 125% = 95% of the original price remains. 95% corresponds to $760, so 1% corresponds to $8 and 100% corresponds to $800.

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