Find no of nuts and raisins. Grandmother made 20 gingerbread biscuits for her grandchildren. She decorated them with raisins and nuts. First she decorated 15 cakes with raisins and then 15 cakes with nuts. At least how many cakes were decorated both with raisins and nuts?

You have $20$ cakes in total, if she decorated $15$ cakes with raisins the least possible number of cakes decorated with nuts and raisins is to decorate first the cakes that have no raisins and then decorate those that already have raisins. So the minimum number of cakes with both raisins and nuts is:

$$15 - 5 = 10$$