Question

Two years ago my age was 4 1/2 times the age of son. 6 years ago ,my age was twice the square of the age of my son . What is the present age of me and my son

Answer 1

if my age is 38 years , my son's age will be 10 years

if my age is 97/8 years , my son's age will be 17/4 years.

Let my age is x and my son's age y.

Case 1 : Two years ago my age was 4 1/2 times the age of son.

i.e., (x - 2) = 4 1/2 (y - 2)

⇒(x - 2) = 9/2(y - 2)

⇒2x - 4 = 9y - 18

⇒9y - 2x = 14 .............(1)

case 2 : 6 years ago , my age was twice the square of the age of my son.

i.e., (x - 6) = 2(y - 6)²

⇒x - 6 = 2y² - 24y + 72

⇒ x = 2y² - 24y + 78 ...........(1)

from equations (1) and (2) we get,

9y - 2(2y² - 24y + 78) = 14

⇒9y - 4y² + 48y - 156 = 14

⇒57y - 4y² - 170 = 0

⇒4y² - 57y + 170 = 0

⇒4y² - 40y - 17y + 170 = 0

⇒(4y - 17)(y - 10) = 0

y = 10, 17/4

x = (9y - 14)/2 = 38, 97/8

hence, if my age is 38 years , my son's age will be 10 years

if my age is 97/8 years , my son's age will be 17/4 years.