The cost of an article is first increased by 20% and then decreased by 30%, find the percentage change in the cost of the article.

Let the cost of the article be 100.

After an increase of 20 %, it becomes = 100 + 20 % of 100

= $100 + \dfrac{20}{100} \times 100$

= $100 + \dfrac{2000}{100}$

= $100 + 20$

= 120

Now it is decreased by 30%, it becomes = 120 - 30 % of 120

= $120 - \dfrac{30}{100} \times 120$

= $120 - \dfrac{3,600}{100}$

= $120 - 36$

= 84

∴ Change on the whole = Final value - Initial value

= 84 - 100

= -16

Change on the whole is negative means change on the whole is decreasing.

∴ Percentage change = $\dfrac{\text{Change on the whole}}{\text{Initial value}} \times 100$ %

= $\dfrac{16}{100} \times 100$ %

= $\dfrac{1600}{100}$ %

= 16%

Hence, the cost of the article is decreased by 16%.