Answer
The majority of ATP in aerobic, eukaryotic cells is produced by the mitochondria .
Explanation :
In the breakdown of sugar (glucose) to carbon dioxide and water, approximately 36 ATP are produced, in three main processes:
Glycolysis, in the cytoplasm, provides a net of 2 ATP (it produces 4, but uses 2),
Krebs Cycle (or Citric Acid Cycle), in the mitochondrion, also produces 2 ATP, as well as electron carriers NADH and FADH2.
The NADH and FADH2 are fed into the Electron Transport Chain in the inner membrane of the mitochondrion, which generates another 32 ATP.
So all but of 36 ATP generated, 34 of them are generated in the mitochondrion.
*Some energy, in the form of ATP and NADH, is used in transporting the products of glycolysis into the mitochondrion, and the process is not always perfectly efficient, hence it is only approximately 36 .