The sum of ages of father and son is 36. If both live until the son becomes as old as his father is now, the sum of their ages becomes 84. Find their present ages.
Ans:
Let the son be x years old presently.
Father's current age = 36 - x
Difference between their ages = 36 - x - x = 36 - 2*x
So it will take the son another (36 - 2*x) years to become as old as the father
is today.
At that time, son's age will be 36 - x (which is the father's present age)
At that time, father's age will be 36 - x + 36 - 2*x = 72 - 3*x

So the sum of their ages will be 36 - x + 72 - 3*x = 108 - 4*x which is given 
to be 84.
So, 108 - 4*x = 84. i.e. 4*x = 24 or x = 6.
Son is  years old, and father is  years old.
Check: For the son to become 30 years old it will take another 24 years. Father
will be 30+24 = 54 years old then. Sum of their ages will be 30 + 54 = 84.
Correct!

Hope this helps :)