The present age of a son is half the present age of his father. Ten years ago, the father was thrice as old as his son. What are their present age?

Let the present age of a father be x years.

Son’s age = (1/2)x years

10 years ago, father’s age was (x − 10) years

10 years ago, son’s age was ((x/2) − 10) years

As per the question, we have

x − 10 = (3x/2) − 30

Transposing 10 on RHS and (3x/2) on LHS, we get

x − (3x/2) = 10 − 30

(2x − 3x)/2 = −20

(−x)/2 = −20

−x = −40

x = 40

Thus, present age of father = 40 years

and age of son = (1/2) × 40 = 20 years.