Question

after 5 year the age of a father will be treble the age of his son while 5 years ago, he was 7 times as old as his son was find their present age

Answer 1

 
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 


present age of son = X
Age of son before 5 years = X-5
So, Present age of father = 7(X-5)+5 ……… (i) 
Age of son after 5 years = X+5
Age of father after 5 years = 3(X+5)
So, present age of father = 3(X+5)-5 ……….(ii)
Equating age of father i.e. (i) and (ii) 
7(X- 5)+5 = 3(X+ 5)-5
7X – 35+5 = 3X + 15-5
7X-3X = 15 - 5 + 35 - 5
4X = 40
X = 40/4 . X (son)= 10 , Father (3(10+5)-5)= 40 yrs 

Answer 2

Let the present age of father be x years
and age of son be y years
After five years
Age of father = x+5
Age of son = y+5
According to the question
x+5=3(y+5)
x+5=3y+15
x-3y = 15-5
x-3y=10 ...(i)
Five years ago
Age of father = x-5
Age of son = y-5
According to the question
x-5= 7(y-5)
x-5= 7y-35
x-7y=-35+5
x-7y = -30 ....(ii)
Subtract equation (ii) from equation (i) we get
4y= 40
y =10
Put the value of y in equation (i)
x-3(10)=10
x-30=10
x= 10 +30
x=40
Hence, the present age of father = 40 years
and the present age of his son = 10 years