three years ago the sum of the age of the father and the sum was 48 years after 3 years the ratio of the ages of the father and son will be 3:1 then how much old is a father from hiss age
Answers
Step-by-step explanation:
Given :-
Three years ago the sum of the age of the father and the son was 48 years after 3 years the ratio of the ages of the father and son will be 3:1 .
To find:-
How much old is a father from his age ?
Solution:-
Let the present age of son be X years
Let the present age of father be Y years
3 years ago their ages would be (X-3) years and (Y-3) years
Given that
Three years ago the sum of the age of the father and the son was 48 years
=> (X-3)+(Y-3) = 48
=> X+Y-6 = 48
=> X+Y = 48+6
=> X+Y = 54 ----------(1)
After 3 years their ages will be (X+3) years and (Y+3) years
Given that
After 3 years the ratio of the ages of the father and son will be 3:1 .
=> (Y+3) : (X+3) = 3:1
=> (Y+3)/(X+3) = 3/1
=> 3(X+3) = Y+3
=> 3X+9 = Y+3
=>3X+9-Y-3 = 0
=> 3X-Y +6 = 0
=> 3X-Y = -6 ---------(2)
On adding (1)&(2)
X+ Y = 54
3X-Y = -6
(+)
_________
4X +0 = 48
_________
=> 4X = 48
=> X = 48/4
=> X = 12 years
On Substituting the value of X in (1)
=> 12+Y = 54
=> Y = 54-12
=> Y = 42 years
Present age of Son = 12 years
Present age of his Father = 42 years
=> 42-12
= 30
Father is 30 years more than his son.
Answer:-
Present age of Son = 12 years
Present age of his Father = 42 years
Father is 30 years more than his son.