The number 350 is first increased by 20% and then decreased by 20%. What is…

Concept

When a value is increased by a percentage x% and then decreased by the same x%, the two changes do not cancel out. The overall multiplying factor is (1 + x/100) × (1 − x/100), which equals 1 − x2/10000 — a number always less than 1. So equal-and-opposite successive percentage changes always leave a net percentage DECREASE, equal to x2/100 percent of the original value.

Application

1. Original value = 350.

2. Increase by 20%: 350 × 1.2 = 420.

3. Decrease this new value by 20% (the second change acts on 420, not on the original 350): 420 × 0.8 = 336.

4. Net change from the original number = 336 − 350 = −14.

5. Percentage change = (−14 ÷ 350) × 100 = −4%, i.e. a 4% decrease.

Cross-check

Using the general result derived above with x = 20: net percentage change = −x2/100 = −(202)/100 = −400/100 = −4%. This matches the step-by-step computation, confirming the answer independently.

The overall change is therefore a 4% decrease.