Two years ago the man's age is 5 times as old as his son.after 2 years his age will be 8 more than 3 times the age of his son. what is the present age of the man and his son
Answers
Answer:
Let the age of man be x and the age of his son be y
x - 2 = 5(y - 2)
x - 2 = 5y - 10
x - 5y = -10 + 2
x - 5y = -8 ----> 1
x + 2 = 3(y + 2) + 8
x + 2 = 3y + 6 + 8
x - 3y = 14 - 2
x - 3y = 12 ----> 2
solving 1 & 2
x - 5y = -8
x - 3y = 12
- + -
-------------
- 2y = -20
y = 20/2
y = 10
substitute y = 10 in equation 2
x - 3y = 12
x - 3(10) = 12
x = 12 + 30
x = 42
So the age of man is x = 42 years and age of his son is y = 10 years..
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Solution
Given :-
- Two years ago the man's age is 5 times as old as his son.
- after 2 years his age will be 8 more than 3 times the age of his son.
Find :-
- Present age of man and his son
Explanation
Let,
- Age of man = x years
- Age of his son = y years
Now, A/C to question
(Two years ago the man's age is 5 times as old as his son. )
==> (x-2) = 5*(y-2)
==> x - 5y = -10 + 2
==> x - 5y = -8 ------------(1)
Again,
(after 2 years his age will be 8 more than 3 times the age of his son.)
==> (x + 2) = 3 * (y+2) + 8
==> x - 3y = 6 + 8 - 2
==> x - 3y = 12 -----------(2)
Subtract equ(1) and equ(2)
==> -5y + 3y = -8 - 12
==> -2y = -20
==>y = -20/(-2)
==> y = 10
Keep Value of y in equ(2)
==> x - 3 * 10 = 12
==> x = 12 + 30
==>x = 42
_____________________
Hence
- Age of man = 42 years
- Age of his son = 10 years
________________
Answer Verification
Case(1).
(Two years ago the man's age is 5 times as old as his son. )
==> (x - 2) = 5 * ( y - 2)
keep Value of x & y
==> 42 - 2 = 5 * (10-2)
==> 40 = 5 * 8
==> 40 = 40
L.H.S. = R.H.S
_______________________
Case(2).
(after 2 years his age will be 8 more than 3 times the age of his son.)
==> (x + 2) = 3 * (y+2) + 8
keep Value of x & y
==> (42 + 2) = 3 * (10+2) + 8
==> 44 = 3 * 12 + 8
==> 44 = 36 + 8
==> 44 = 44
L.H.S. = R.H.S .
Here, both case are satisfy .
So, we can say that Age of man and Age of his son is right .