five year ago a man was 6 times the square of his sons age after four years he will be 3 times the age of his son find his age
Answers
Step-by-step explanation:
Given :-
Five year ago a man was 6 times the square of his sons age after four years he will be 3 times the age of his son .
To find :-
Find his age ?
Solution :-
Let the present age of the son of a man be
X years
Let The present age of the man be Y years
The age of his son 5 years ago = (X-5) years
The age of the man 5 years ago = (Y-5) years
Five years ago his age = 6 times the square of his sons age
=> Y-5 = 6(X-5)² years
=>Y-5 = 6(X²-2(X)(5)+5²)
=>Y-5 = 6(X²-10X+25)
=>Y-5 = 6X²-60X+150
=> Y = 6X²-60X+150+5
=> Y = 6X²-60X+155 ------(1)
And
The age of his son after 4 years = (X+4) years
The age of the man after 4 years = (Y+4) years
Age of the man after 4 years = 3 times the age of his son
=> Y+4= 3(X+4) years
=> Y+4 = 3X+12years
=> Y = 3X+12-4
=> Y = 3X +8 years ------------(2)
From (1) &(2)
=> 6X²-60X+155 = 3X+8
=> 6X²-60X+155-3X-8 = 0
=> 6X²-63X+147 = 0
=> 6X²-42X-21X+147 = 0
=> 6X(X-7)-21(X-7) = 0
=> (X-7)(6X-21) = 0
=> X-7 = 0 or 6X-21 = 0
=> X = 7 or 6X = 21
=> X = 7 or X = 21/6
=> X = 7 or X = 7/2
X can not be equal to fraction
Therefore, X = 7 years
The present age of his son = 7 Years
On Substituting the value of X in (2)
=> Y = 3(7)+8
=> Y = 21+8
=> Y = 29 years
The age of the man = 29 years
Answer:-
The present age of the man = 29 years
Check:-
The present age of his son = 7 Years
The present age of man = 29 years
The age of his son 5 years ago = 7-5 = 2years
The age of the man 5 years ago = 29-5 = 24years
Five years ago his age = 6 times the square of his sons age
=> 24= 6(2)² years
=> 24 = 6×4
=> 24 = 24 years
The age of his son after 4 years =7+4 = 11 years
The age of the man after 4 years = 29+4 =
33 years
Age of the man after 4 years = 3 times the age of his son
=> 33= 3(11) years
=> 33 = 33 years
Verified the given relations in the given problem.