Meg started with the number 100. She increased this number by $20 \%$ and then increased the resulting number by $50 \%$. Her final result was
(A) 120
(B) 240
(C) 187.5
(D) 200
(E) 180
$20 \%$ of the number 100 is 20 , so when 100 is increased by $20 \%$, it becomes $100+20=120$.

$50 \%$ of a number is half of that number, so $50 \%$ of 120 is 60 .

Thus, when 120 is increased by $50 \%$, it becomes $120+60=180$.

Therefore, Meg's final result is 180 .

ANSWER: (E)