A store increases price by 10% and then decreases by 10%. Is the final price higher, lower, or the same as the original?

A store increases price by 10% and then decreases by 10%. Is the final price higher, lower, or the same as the original?

• A. Lower by 1%
• B. Higher by 1%
• C. The same as the original
• D. Lower by 0.5%

Answer: (A)

The final result comes from multiplying the two percentage changes. A 10% increase turns the price into 1.10 of its original amount, and a 10% decrease uses 0.90 of that new amount. So the final price is 1.10 × 0.90 = 0.99 of the original. In other words, the price ends up 99% of what it started with, which is 1% lower overall. For example, starting at 100, you rise to 110, then fall by 10% of 110 (which is 11) to 99. The smaller final amount happens because the second change applies to the increased price, not the original. The net effect is a 1% decrease.

The final result comes from multiplying the two percentage changes. A 10% increase turns the price into 1.10 of its original amount, and a 10% decrease uses 0.90 of that new amount. So the final price is 1.10 × 0.90 = 0.99 of the original. In other words, the price ends up 99% of what it started with, which is 1% lower overall. For example, starting at 100, you rise to 110, then fall by 10% of 110 (which is 11) to 99. The smaller final amount happens because the second change applies to the increased price, not the original. The net effect is a 1% decrease.