Question

20 years ago, Mike was four times as old as John. Four years ago now, Mike will be twice as old as John. Let x represent the Mike's age and y represent the John's age.

Answer 1

Let x represent the Mike's age and y represent the John's age. Then, 20 years ago, Mike was x-20 years old and John was y-20 years old so that x-20 = 4(y-20) or, x= 4y +20-80 or, x = 4y-60…(1).

Also, 4 years from now, Mike will be x+4 years old and John will be y+4 years old so that x+4= 2(y+4) or, x = 2y+8-4 or, x = 2y+4…(2). On comparing these 2 equations, we get 4y-60 = 2y+4 or, 2y = 60+4 = 64 so that y = 64/2 = 32. Then, from the 2^nd equation, we have x = 2*32+4 = 64+4 = 72.

Thus, Mike's age is 68 years and John's age is 32 years.