Question

2years ago fathsr was three times as old as his son and two years hence twice his age will be equal to five times that of his son find the present ages

Answer 1

Let
Present age of Father = f
Present age of Son = s

Two years ago
f-2=s-2
Father was 3 times as old as his son
f-2=3(s-2)
f-2=3s-6
f=3s-6+2
f=3s-4............(1)
and 2 year hence,
f+2=s+2
then twice his age will be equal to 5 times that of his son
2(f+2)=5(s+2)
2f+4=5s+10
2f=5s+10-4
2f=5s+6.............(2)
Put the value of f in (2) from (1)
2(3s-4)=5s+6
6s-8=5s+6
6s-5s=6+8
s=14
Put the value of s in (1)
f=3s-4............(1)
f=3(14)-4
f=42-4
f=38


Father's age is 38
Son's age is 14

Answer 2

Let father's age =x, son's age=y
x-2=3(y-2)
x-2=3y-6
x-3y=-4
2(x+2)=5(y+2)
2x+4=5y+10
2x-5y=6
2x-6y=-8
y=14
x-42=-4
x=38
Father is 38 years old.
Son is 14 years old.