Question

five years ago a man was 7 times as old as his son. five years hence, the father will be three time as old as his son. find their present age?

Answer 1

Sons age 5 years ago=x father's age = 7x
their present age = x+5 and 7x+5 resp
Sons age 5 years hence = x+10(since x is sons age 5 years ago from present age and we are talking of his age 5 years hence from his present age so 5+5=10)
fathers age 5 years hence =3(x+10)
hence the fathers present age will be 3(x+10)-5
also fathers present age =7x+5
therefore 7x+5=3(x+10)-5
7x+5=3x+30-5
7x-3x=25-5
4x=20
x=5
sons age 5 years ago=5years fathers age =5*7=35years
present age of the son=10years(5+5) fathers age=35+5=40 years
sons age 5 years hence= 5+10=15years fathers age =3*(5+10)=45 years