If adults cut set X and children cut set Y, then:

2.4x+y = 25 (both x and y are natural numbers greater than 0)

Because the coefficient of y is 1, that is, y is an integer,

So 2.4x is also an integer.

So one digit of x is 5 or 0,

When x=5, 2.4x= 12, then y=25-2.4x= 13.

When x= 10 and 2.4x=24, then y=25-2.4x= 1.

That is, 5 sets of adult scissors, 3 sets of children scissors 13 sets or adult scissors 10 sets and children scissors 1 set.