Question

Five years ago, a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

Answer 1

Five years ago:

Let the age of the son be x years.

Therefore, the age of the father will be 7x years. 

Thus, Present age of the son = (x + 5) years, and Present age of the father = (7x + 5) years,

After five years:

Age of the son = (x + 5 + 5) = (x + 10) years,

Age of the father = (7x + 5 + 5) = (7x + 10) years,

According to the given question,

7x + 10 = 3(x + 10)

7x − 3x = 30 − 10

4x = 20

∴ x = 5

Thus, Calculation of the ages,

(x + 5) years

= (5 + 5)

= 10 years,

(7x + 5) years

= (7 × 5 + 5)

= 40 years,

Hence, the present ages of the son and his father are 10 years and 40 years, respectively.