Question

The age of father 3 years ago was 4 times the age of his sin. If 3 years hence the father would be 3 times that of his son

Answer 1

let age of father be x qnd that of son be y.
CASE 1
fathers age 3 years ago= (x-3)
sons age 3 years ago = (y-3)
ATQ,
x-3= 4(y-3)
x-3= 4y-12
x-4y= -12 + 3
x -4y = -9 -----------(1)

CASE 2
fathers age 3 years hence = (x+3)
sons age 3 years hence = (y+3)

ATQ,
x+3 = 3(y+3)
x+3 = 3y+9
x-3y = 9-3
x- 3y = 6 -----------(2)

eliminating the two equations

x-4y= -9
x-3y= 6
_______
(-) (+) (-)
-y = -15
y = 15
putting value of y in eq (2)

x -3(15)= 6
x-45 = 6
x = 6+45
x= 51

therefore age of father is 51 years and that of son is 15 years.

hope it helps you.