Arunner is competing in a 10km track meet and just before completing the race the runner is nearly out of breath and the energy needed to finish the race ,which cell structure is most affected by this lack of energy

We know that the mitochondria inside a cell are the "energy powerhouses" of the cell - they produce a large amount of ATP that is then used by the cells.

When someone runs, the mitochondria in that person's cells must work continuously harder in order to provide the necessary ATP (energy) that is required in order for that person to continue running.

Since this person in the question has just run a 10 km track meet, we can assume that they are very tired, and the question tells us that they are lacking energy.

This is mostly due to the mitochondria inside the cell as we have just gone over.