Two years ago, a man's age was three times the square of his son's age. In three years time his age will be four times his son's age. Find their present ages
Answers
Let the age of his son two years ago was x years and therefore according to the question his ( father's ) age would be 3 times the square of his son's age, so father's age = 3 x^2 years
Age of father 2 years ago = 3x^2 years
Age of his son 2 years ago = x years
Given that in three years age of father will be four times his son's age, according to the question 2 years their age was 3x^2 years and x years, so now their age will be 2 years more .
Present age of father = ( 3x^2 + 2 ) years
Present age of son = ( x + 2 ) years
Age of father after 3 years = ( 3x^2 + 2 + 3 ) years = ( 3x^2 + 5 ) years
Age of son after 3 years = ( x + 5 ) years
Given, Age of father after 3 years = 4 times the age of his son
( 3x^2 + 5 ) years = 4( x + 5 ) years
3x^2 + 5 = 4x + 20
3x^2 - 4x + 5 - 20 = 0
3x^2 - 4x - 15 = 0
3x^2 - ( 9 - 5 )x - 15 = 0
3x^2 - 9x + 5x - 15 = 0
3x( x - 3 ) + 5( x - 3 ) = 0
( x - 3 ) ( 3x + 5 ) = 0
So, x - 3 = 0 Or 3x + 5 = 0
x was assumed as age therefore age cannot be negative, value of x will be positive.
x = 3
Hence,
Present age of son = x years = 3 years
Present age of father = 3x^2 years = 3( 3 )^2 years = 27 years