The sum of the ages of a brother and sister at present is 21. Five years ago the product of their ages was 28. What is the age of the brother and the sister?

Let the current ages of the brother and sister be x and y.
Given:

x+y=21⟹y=21−x
Five years ago, their ages were (x−5) and (y−5).
Given:

(x−5)(y−5)=28
Substitute y=21−x into the equation:

(x−5)(21−x−5)=28
(x−5)(16−x)=28
16x−x
2
−80+5x=28
−x
2
+21x−80=28
x
2
−21x+108=0
Solving the quadratic equation:

(x−9)(x−12)=0
So, x=9 or x=12.

If x=9, then y=12. If x=12, then y=9.
Thus, the ages are 9 and 12.