There are 57 guests and he want everyone to have a slice. i want to pay as little as possible and for them to be the same size. 20cm cake serves 12 people. 13.50 per cake, 25cm cake, serves 20 people at 18.75 per

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.