Question

Five years ago a man was eight times as old as his son. Five years hence, the father will be thrice the age of his son. Find their present age

Answer 1

Let the age of the father be x

let the age of the son be y

case I

age of father five years ago = x - 5

age of son five years ago = y - 5

ATQ, x - 5 = 8(y - 5)

         x - 5= 8y - 40

          x - 8y = -45                                  (1)

case II

ago of father fiver years later = x +5

age of son 5 years later = y+5

ATQ, x +5 = 3(y +5)

         x +5 = 3y + 15

          x - 3y = 10                                       (2)

on subtracting eq (2) from eq(1), we get

 y = 11

on substituting y=11 in equation (1), we get

x- 8 x 11 = -45

x - 88 = -45

x = 43

therefore the age of father, x = 43

and age of son,y = 11