Mathematics·Percentages·grades 6–9

An item went up 20%, then down 20% — how did the price change?

Problem

The price of an item first rose by 20%, and then the new price fell by 20%. By what percentage does the final price differ from the original one?

Answer

The final price is 4% below the original one

Step-by-step solution

Step 1. Denote the initial price
Let the initial price be 100 (a convenient number — percentages are easier to compute). Everything else is expressed in terms of it.
Step 2. An increase of 20%
After the rise of 20% the price became $100 \cdot 1.2 = 120$ .

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Step 3. A decrease of 20%
Step 4. Compare with the start

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Common mistakes

Assuming that +20% and −20% cancel each other out and the price does not change — that is wrong.
Taking the second percentage from the initial price instead of from the new one.

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After a 15% discount an item costs 2550 ₪ — what was the price before the discount?grades 6–9A deposit of 50 000 ₪ at 10% a year with compounding — how much after 2 years?grades 9–11

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