Why is 20 percent off an item plus an additional 20 percent off not 40 percent?

Answer 1

Because the second discount refers to the already-discounted price,

not to the original full price.

Example:

-- The item was originally priced at $100.

-- It was discounted 20%, and that brought its price down to $80.

-- If it's discounted again later, then the second 20% discount will be 20% of $80,

not 20% of $100.

20% of $80 is $16, so the second discount will reduce the price to $64.

-- If it had been reduced from $100 all the way to $64 in one cut the first time,

that discount would have been 36% .