Question

father was 3 times as old as his son and two years hence twice his age will be equal to five times that of his son find their present age

Answer 1

Hi,Happy to help You
Here is your Solution:-
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 
Present age of Father = f = 38 years old
Present age of Son = s = 14 years old 
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Answer 2

Let son's age = x

Two years ago son's age= x-2.

His Father's age at that time = 3(x-2).

Present age of Father = 3x-6+2=3x-4

Two years hence father's age=3x-4+2=3x-2.

Two years hence son's age = x+2.

Given :-5*(x+2)=2*(3x-2)

5x + 10= 6x - 4

10+4=6x-5x

14=x

SON'S PRESENT AGE : 14 years.

FATHER'S PRESENT AGE: 38 years.