Five years age 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.

Explanation

Let present age of son be x years and the present age of father by y years.
Five years hence, the age of son = x + 5
and the age of father = y + 5
Using given information
3(x + 5) = y + 5
implies 3x - y = - 10 ….(1)
Five years ago, age of son = (x - ) years
and age of father = (y - 5) years
`therefore 7(x - 5) = y - 5`
implies 7x - y = 30 ...(2)
Subtracting equation (1) from (2), we get
4x = 40
implies x = 10
On substituting x = 10 in equation (1)
`3 xx 10 - y = - 10`
implies 30 - y = - 10
implies - y = - 40
implies y = 40
Hence, present age of son is 10 years and present age of father is 40 years.