If a quantity increases by 25% and then decreases by 20%, what is the net change relative to the original value?

If a quantity increases by 25% and then decreases by 20%, what is the net change relative to the original value?

• A. -5%
• B. 5%
• C. 10%
• D. 0% (zero net change)

Answer: (D)

Percent changes stack multiplicatively. An increase of 25% multiplies the original amount by 1.25, and then a decrease of 20% multiplies the new amount by 0.80. The overall effect is 1.25 × 0.80 = 1.00, which means you end up exactly where you started. For example, if you begin with 100, a 25% rise takes you to 125, and a 20% drop on 125 is 25, bringing you back to 100. So the net change relative to the original value is 0%.

Percent changes stack multiplicatively. An increase of 25% multiplies the original amount by 1.25, and then a decrease of 20% multiplies the new amount by 0.80. The overall effect is 1.25 × 0.80 = 1.00, which means you end up exactly where you started.

For example, if you begin with 100, a 25% rise takes you to 125, and a 20% drop on 125 is 25, bringing you back to 100. So the net change relative to the original value is 0%.