The sum of the ages of a father and a son presently is 70 years. After 10 years the son's age is exactly half that of the father's. What are their ages now?

Suppose the present age of son = P years
The present age of father = Q years
P + Q = 70 ...(i)
According to question, 2(P + 10) = Q + 10
⇒ 2P + 20 = Q + 10
⇒ 2P – Q = –10 ....(ii)
From equations (i) and (ii) , we get
3P = 70 – 10 = 60 ⇒ P = 20 years
∴ Q = 70 – 20 = 50 years