A washing machine's price is increased by 25% and then decreased by 25%. What is the net percentage change in price?

The new price after the increase is $P_1$.

$$P_1 = P + (0.25 \times P) = 1.25P$$

The final price after the decrease is $P_2$.

$$P_2 = P_1 - (0.25 \times P_1) = 0.75P_1$$

Substitute the value of $P_1$ from Step 2:

$$P_2 = 0.75 \times (1.25P)$$ $$P_2 = 0.9375P$$

The net change is the difference between the final price and the original price, expressed as a percentage of the original price.

$$\text{Net Change} = \frac{P_2 - P}{P} \times 100\%$$ $$\text{Net Change} = \frac{0.9375P - P}{P} \times 100\%$$ $$\text{Net Change} = \frac{-0.0625P}{P} \times 100\%$$ $$\text{Net Change} = -0.0625 \times 100\%$$ $$\text{Net Change} = -6.25\%$$

A negative sign indicates a decrease.

The net change in price will be a 6.25% decrease.

The final answer is \text{6.25% decrease}.