You have been invited to attend an interview for a place studying a course in a college. Unfortunately because of a previous appointment you cannot come at the time they wish.
Write a letter to the admissions tutor and explain your position. Apologise and offer to come on another day or later the same day. Ask also how long the interview will be and whether there will be any tests during it.
Thank you very much for your letter dated 15th May inviting me for an interview at your college on Wednesday 2nd June at 10am. I am extremely sorry but I am unable to come to an interview at that time because I have a maths exam that morning. It really cannot I miss this exam but of course I really wish to attend the interview with you. Is it possible that I could come to the interview the same day but in the afternoon? Failing that, I would be able to come the next day or any day after.
I would also like to ask some things about the interview. I would like to know how long it will last and also whether I will be required to do any tests during it.
Once again I apologise for not being able to attend the interview at the time that you wanted and I hope I will be able to meet with you at another time.
I look forward to hearing from you soon.