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 3 of 8.
Rass said:
8 years ago
The age of A and B three years ago were 'x' and 'y+2' years, therefore the sum of their ages 4 years hence will be?
Can someone solve this?
Can someone solve this?
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?
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.
Alekhya said:
8 years ago
Father = 60-x.
6 years ago so (-) symbol if it is after 6 years means we add (+) symbol.
We add 6 to both sides,
(60-x)-6 = (x-6).
Here ques asked father's age was five times the age of the son
So,
(60-x)-6 = five times of(x-6) /(x-6) is sons age)/.
(60-x)-6 = 5(x-6).
54-x = 5x-30.
6x = 84.
x = 84/6.
x = 14.
After 6 years, son's age will be:
Son age x.
After six years so;
x+6.
14+6 = /20 years/.
6 years ago so (-) symbol if it is after 6 years means we add (+) symbol.
We add 6 to both sides,
(60-x)-6 = (x-6).
Here ques asked father's age was five times the age of the son
So,
(60-x)-6 = five times of(x-6) /(x-6) is sons age)/.
(60-x)-6 = 5(x-6).
54-x = 5x-30.
6x = 84.
x = 84/6.
x = 14.
After 6 years, son's age will be:
Son age x.
After six years so;
x+6.
14+6 = /20 years/.
Haider said:
8 years ago
We can solve it by this method.
The sum of the ages =60
six years ago
we will subtract 12 years, 6 year each,
then sum would be 48.
divide by 6, bco s they are in the ratio of 1:5.
8 : 40 would be the answer,
Add 12 years to 8 and we get 20.
The sum of the ages =60
six years ago
we will subtract 12 years, 6 year each,
then sum would be 48.
divide by 6, bco s they are in the ratio of 1:5.
8 : 40 would be the answer,
Add 12 years to 8 and we get 20.
G.Bharath Reddy said:
8 years ago
Simple steps:
Let the ages of father and be y,x;
x+y+6=60;
Before 6 years,fathers age was x+6=5x+6
x+6+5x+6=60;
6x+12=60;
6x=48;
x=8;
So,son age is 8yrs;
At that moment,son age is=8+6=14yrs;
After 6yrs=14+6;
20 yrs/.
Let the ages of father and be y,x;
x+y+6=60;
Before 6 years,fathers age was x+6=5x+6
x+6+5x+6=60;
6x+12=60;
6x=48;
x=8;
So,son age is 8yrs;
At that moment,son age is=8+6=14yrs;
After 6yrs=14+6;
20 yrs/.
Akshay said:
8 years ago
Simple Steps:
The Sum of Father and Son age: F+S=60.
Before 6 years condition: F-6=5(S-6); F=5S-24,
Put F in F+S=60 i.e,
5S-24+S=60 ; S=14
After Six years, S=14+6 = 20.
The Sum of Father and Son age: F+S=60.
Before 6 years condition: F-6=5(S-6); F=5S-24,
Put F in F+S=60 i.e,
5S-24+S=60 ; S=14
After Six years, S=14+6 = 20.
Shaila said:
8 years ago
Thank you everyone for explaining the solution.
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.
BHARATH said:
9 years ago
@All.
Let father & son's age be x&y.
As said present sum of x + y = 60.
& six yrs ago father's age was five times the age of his son i. e
(x-6) = 5(y-6)>>>eq 1.
x + y = 60>>we can ryt this as x = 60 - y.
So, substitute x value in eq 1.
(60 - y - 6) = 5(y - 6)
54 - y = 5y - 30
54 + 30 = 5y + y
84 = 6y.
So,
y = 84/6 = 14,
y = 14.
And y's age after 6 yrs =(y + 6).
= 14 + 6 = 20yrs.
So answer is D
Let father & son's age be x&y.
As said present sum of x + y = 60.
& six yrs ago father's age was five times the age of his son i. e
(x-6) = 5(y-6)>>>eq 1.
x + y = 60>>we can ryt this as x = 60 - y.
So, substitute x value in eq 1.
(60 - y - 6) = 5(y - 6)
54 - y = 5y - 30
54 + 30 = 5y + y
84 = 6y.
So,
y = 84/6 = 14,
y = 14.
And y's age after 6 yrs =(y + 6).
= 14 + 6 = 20yrs.
So answer is D
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