3 cakes of 25cm will be enough for all and it will cost him least possible amount of 3 x 18.75 = 56.25
as
1 cake of 25cm serves 20 people
3 cakes of 25cm will serve 3 x 20 = 60 people
3 cakes will be more than enough for 57 guests and himself as well, so it will be served in overall 58 persons and it will cost him:
56.25 / 58 = 0.97 per guest.
Which will be the least cost for him.