3 years ago, the sum of ages of a father and his son was 40 years. After 2 years the sum of ages of the father and his son will be

Let the present ages of father and son be x years and y years respectively.

Age of father three years ago = x – 3

Age of son three years ago = y – 3

According to the question,

x – 3 + y – 3 = 40

⇒ x + y = 40 + 6

⇒ x + y = 46 .. (i)

After 2 years,

Age of father = x + 2

Age of son = y + 2

Sum of their ages after 2 years = x + 2 + y + 2 = (x + y) + 4 = 46 + 4 = 50 {Using (i)}