How should a customer representative respond when they do not know the answer to a question?

The best way is to honestly accept that currently you do not know the answer and ask for a little time from customer and promise him/her that you will get back with the answer and then consult your senior or any other person who would be knowing the answer and as promised get back to the customer and clarify the doubt.Initially this might create a negative impression in customer's mind but eventually when you will be back with answer, the positive impression will be created in customer's mind that unlike other representatives who put forward wrong information if they do not know something, this representative has taken pain of clarifying my point and this positive impression will dilute the negative impression which was created earlier. In short be honest, find the solution to the query and get back to the customer at the earliest.