Question

A number is first increased by $20\%$ and the resulting number is then decreased by $10\%$. Find the overall change in the number as percent.

Answer 1

Let the original number $=100$
Increased percent $=20\%$
$\therefore$ New number $=100+20\%\times 100=100+20=120$
Decreased percent $=10$
$\therefore$ New number $=120-10\%\times 120=120-12=108$
Overall change $=108-100=8$
Therefore, final increase percentage $=\frac{8}{100}\times 100=8\%$