I would apologize for the delay and simply answer the question for the customer. I wouldn't say why there was a delay at all- the customer will probably just be happy with the answer. If it was in my power to offer them something for the delay I would do so.
If the customer pushed me for an explanation on why it took so long I would be honest and say "I don't know why it took so long but you can rest assured I will make my manager/supervisor aware of this issue so it does not happen again."
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