Explanation:

Correct Answer is (c).The given sentence implies that he is late and somebody else has been waiting for a long time for me. It an action is still going on at the present time starting from some point of time in the past, the present perfect continuous tense is used for that action. Here, the person has been waiting for a long time but he is yet to come. That means the action is still in progress.
Now, he is latest is completely wrong since this does not imply anything meaningful. He is late makes senses in this context whereas are waiting is in present continuous tense and therefore, is not correct in the present context of the sentence, present perfect continuous tense should be used in this sentence i.e. have been waiting.
The correct sentence would be: I am really sorry that he is late; you must have been waiting for a long time.This makes option C the correct choice among the given options.