Aptitude - Problems on Ages - Discussion
Discussion Forum : Problems on Ages - General Questions (Q.No. 8)
8.
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
Answer: Option
Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 6 years = (x+ 6) = 20 years..
Discussion:
71 comments Page 2 of 8.
Akash said:
9 years ago
6 years ago their age ratio was 5x : x right?
Then to find thier present age add 6yeras to both of them,
Now it becomes 5x+6 : x+6.
A/c data sum of their present age is equal to 60.
Now. 5x+6(father's age) + x+6(son's age) =60.
i.e 5x+6+x+6 = 60,
6x+12 = 60,
6x = 48,
x = 8.
x is son's age six years ago;
Son's present age is 8 + 6 =14.
Son's age after 6years from present is 14+6 = 20.
Then to find thier present age add 6yeras to both of them,
Now it becomes 5x+6 : x+6.
A/c data sum of their present age is equal to 60.
Now. 5x+6(father's age) + x+6(son's age) =60.
i.e 5x+6+x+6 = 60,
6x+12 = 60,
6x = 48,
x = 8.
x is son's age six years ago;
Son's present age is 8 + 6 =14.
Son's age after 6years from present is 14+6 = 20.
Anil said:
8 years ago
Present age of F+S=60.
F=60-S.
6 years ago age of F+S=60-6-6=48-----(1)
and 6years ago son age is (s-6) and father age is 5(s-6).
Substitute these are in eq(1).
5(s-6)+(s-6)=48,
5s-6s+s-6=48,
Present age of son is S=14.
From F=60-s,
=>F=60-14,
Present age of father F=46.
After 6years son age is S=14+6
S=20 years.
After 6 years father age is F =46+6=52.
F=60-S.
6 years ago age of F+S=60-6-6=48-----(1)
and 6years ago son age is (s-6) and father age is 5(s-6).
Substitute these are in eq(1).
5(s-6)+(s-6)=48,
5s-6s+s-6=48,
Present age of son is S=14.
From F=60-s,
=>F=60-14,
Present age of father F=46.
After 6years son age is S=14+6
S=20 years.
After 6 years father age is F =46+6=52.
Nandhini said:
1 decade ago
@Sunil.
Case I is right.
Logically father's age should be more than son's age.
So 4x is greater than x so its right to take son's age x and father's age 4x.
Case-II is logically wrong.
Let x=20 i.e father's age then
Son's age will be 80 i.e 4x.
How could a 20yrs father can have 80 yrs son.
Hence case - I is right sons age x and fathers age 4x.
Case I is right.
Logically father's age should be more than son's age.
So 4x is greater than x so its right to take son's age x and father's age 4x.
Case-II is logically wrong.
Let x=20 i.e father's age then
Son's age will be 80 i.e 4x.
How could a 20yrs father can have 80 yrs son.
Hence case - I is right sons age x and fathers age 4x.
Sudha said:
1 decade ago
We can solve like this also:
Father is mentioned as 'f'.
Son is mentioned as 's'.
Sum of father and son age ==> f+s = 60 ----- (1).
Before 6 years ==> (f-6) = 5(s-6).
F-5s = -24 -------------- (2).
Solve equation 1 and 2 we can get the value of s = 14.
The current age of son is ===> 14.
After 6 year ==> 14+6 = 20.
Father is mentioned as 'f'.
Son is mentioned as 's'.
Sum of father and son age ==> f+s = 60 ----- (1).
Before 6 years ==> (f-6) = 5(s-6).
F-5s = -24 -------------- (2).
Solve equation 1 and 2 we can get the value of s = 14.
The current age of son is ===> 14.
After 6 year ==> 14+6 = 20.
Vikas said:
8 years ago
Let the ratio of father and son 6 years ago was 5x:x.
Both father and son age's sum 6 years ago was,
60-12=48,
Then, 5x+x=48,
6x=48,
x=8.
Father age was 5*8=40 and son's age was 8.
At present father age is 40+6=46 and son's age is 8+6=14.
At present father and son's age some 46+14=60.
Then how the son's age is 20?
Both father and son age's sum 6 years ago was,
60-12=48,
Then, 5x+x=48,
6x=48,
x=8.
Father age was 5*8=40 and son's age was 8.
At present father age is 40+6=46 and son's age is 8+6=14.
At present father and son's age some 46+14=60.
Then how the son's age is 20?
Selvi.k said:
1 decade ago
We will solve this problem by solving the two equation
Consider son's age=Y, Fathers age=X.
Let X+Y=60. (1)
6 years ago means
Son's age=X-6, Fathers age=Y-6.
So the equations changed as per the condition
5Y-6=X-6.
We get,
X-5Y=-24. (2).
Solve (1) , (2).
We get y=14, x=46.
After 6 years the son's age=14+6=20.
Consider son's age=Y, Fathers age=X.
Let X+Y=60. (1)
6 years ago means
Son's age=X-6, Fathers age=Y-6.
So the equations changed as per the condition
5Y-6=X-6.
We get,
X-5Y=-24. (2).
Solve (1) , (2).
We get y=14, x=46.
After 6 years the son's age=14+6=20.
Nish said:
9 years ago
Age of the son 6 years ago = 'X'.
Age of the father 6 years ago = '5X'.
At present sum of the father and son's age = (X + 6) + (5X + 6) = 60.
=> X = 8 which is assumed as the age of 6 years ago so, at present age of the son is X + 6 i.e 8 + 6 = 14.
After 6 years age of the son will be = 14 + 6 = 20 years.
Age of the father 6 years ago = '5X'.
At present sum of the father and son's age = (X + 6) + (5X + 6) = 60.
=> X = 8 which is assumed as the age of 6 years ago so, at present age of the son is X + 6 i.e 8 + 6 = 14.
After 6 years age of the son will be = 14 + 6 = 20 years.
Amit said:
2 decades ago
We can also solve this as below:
Let six years ago son's age be x, and fathers age be 5x.
Then sum of their present age
(x+6)+(5x+6)=60
x+5x+12=60
6x+12=60
6x=60-12
6x=48
x=8
Hence six years ago son's age was 8 years
and present age is 8+6=14 years
Answer=after six years his age will be 14+6=20 years.
Let six years ago son's age be x, and fathers age be 5x.
Then sum of their present age
(x+6)+(5x+6)=60
x+5x+12=60
6x+12=60
6x=60-12
6x=48
x=8
Hence six years ago son's age was 8 years
and present age is 8+6=14 years
Answer=after six years his age will be 14+6=20 years.
(2)
Shafeen Ahmed said:
3 months ago
Solution using options:
6 years back Son's age: Minus 12 from each option.
So: 0 2 6 8.
6 years back sum of the father's and son's age = 60 - 6 - 6 = 48,
6 years back relationship of age; F = 5s.
If s = 8, F = 5 * 8 = 40;
Total = 40 + 8 = 48 (Verified).
After 6 years, son's age = 8 + 12 = 20.
6 years back Son's age: Minus 12 from each option.
So: 0 2 6 8.
6 years back sum of the father's and son's age = 60 - 6 - 6 = 48,
6 years back relationship of age; F = 5s.
If s = 8, F = 5 * 8 = 40;
Total = 40 + 8 = 48 (Verified).
After 6 years, son's age = 8 + 12 = 20.
Vidyaram meena said:
7 years ago
There is another way to solve the same problem.
Let's suppose son age y and father age x.
according to question
x+y=60 ----> eqn(1).
and
x-6=5(y-6).
x-5y=-24----> equ(2).
By solving eqn(1) and eqn(2) we get y=14.
From question.
Then, y+6=14+6=20.
Hence after 6 years, the age of son is 20.
Let's suppose son age y and father age x.
according to question
x+y=60 ----> eqn(1).
and
x-6=5(y-6).
x-5y=-24----> equ(2).
By solving eqn(1) and eqn(2) we get y=14.
From question.
Then, y+6=14+6=20.
Hence after 6 years, the age of son is 20.
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