Answer: The required discount is $819 and the rate of discount is 20.48%.
Step-by-step explanation: Given that a home theater system is marked down from $3999 to $3180.
We are to find the discount and the rate of discount.
The discount will be given by actual price minus the marked price.
We have
Actual price = $ 3999 and marked price = $3180.
So, the discount is given by

And the rate of discount is

Thus, the required discount is $819 and the rate of discount is 20.48%.