Question

If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is,

• A. Decrease of 99%
• B. No change
• C. Decrease of 1 %
• D. An increase of 1%
• E.

Hint:

When a price is decreased and then increased by the same percentage, the net effect will always be a decrease. Use multiplication to find the new price after each change.

Answer 1

The Correct Option is C

Assume the original price of the item is \( x \). 

Step 1: The price is first reduced by 10\%. The new price becomes: \[ x - 0.10x = 0.90x \] 

Step 2: After this reduction, the price is increased by 10\%. The new price after this increase is: \[ 0.90x + 0.10 \times 0.90x = 0.90x \times 1.10 = 0.99x \] 

Step 3: Comparing the final price \( 0.99x \) to the original price \( x \), we observe that the price has decreased by \( 1\% \). Thus, the net effect on the price is a decrease of \( 1\% \).