The total of the ages of father and son is 55 years. If the father was to live till his son's age equals his present age, the total of their ages would be 93 years. Find their present ages.

Explanation

We know that the sum of ages of two persons will not be the same everytime. But the difference of their ages remains the same forever. Using this concept we will solve this problem. First of all we make a rough sketch.

When age of son will be 55 - x, then what will be the age of father. Let at that time father will be of y years. So, difference of their ages will remain 55 - 2x years.
`therefore y - (55 - x) = 55 - 2x`
implies y = (55 - 2x) + (55 - x) = 110 - 3x
Now, according to the problem,
(55 - x) + (110 - 3x) = 93
implies 165 - 4x = 93
implies 4x = 72
implies x = 18
`{:(therefore " Present age of son = 18 years."),("and present age of father = 55 - 18 = 37 years."):}}`