Agerbil cage, priced at $18, is discounted 20% for one week, and then this price is marked up 20%. is the price back to 20% explain

No, it isn't!

first, the discount is 20 percent of 18 dollars, that is 18/5=3.6

this means that during the first week the prize is 18-3.6=14.4

now, the prize is marked up 20 % of 14.4! this is 2.88

so the prize later will be 14.4+2.88, that is 17.28, not 18

what is relevant here is what a number is a percent OF

The answer to your question is 1/9