Question

Three years ago, the age of a man is the square of the age of his son , Six years hence , the

age of the man will be three times the age of his son. Find the present age of the man and

the age of his son three years ago.​

Answer 1

Let the man's current age be x and that of his son be y

From first condition,

(x−2)=3 {y-2}^{2} . ----------(1)

From the second condition,

(x+3)=4(y+3)

x+3=4y+12

x=4y+9 ------------(2)

put the value of x from equation 2 to 1

4y+9−2=3 {y}^{2} +4−4y)

3y^2−16y+5=0

3y^2 −15y−y+5=0

3y(y−5)−1(y−5)=0

(3y−1)(y−5)=0

so, y= 3/1 . which is not possible

and y=5

son's age x=5 years

father's age =4(5)+9=29 years.

(from equation 1)