five years hence father's age will be three times his son's age then , five years ago father's age was seven times his son's age then find their present ages

Let the father's age be x and the son's age be y

 

Five years hence:

Father's age = x+5

Son's age = y+5

Given: x+5 = 3(y+5)

That is x - 3y = 10   ....(1)

 

Five years ago:

Father's age = x - 5

Son's age = y - 5

Given: x - 5 = 7(y - 5)

That is x - 7y = -30   ....(2)

 

Solving the two simultaneous equations we have

x = 40 and y = 10

 

Thus the present ages of father and son are 40 and 10