Aptitude - Problems on Ages - Discussion

Sum of present ages of a father and his son is 60 years.
Son + Father = 60

Six years ago:

Son + father = 60 - 12( six years ago means son-6 and father-6 )
Son + father = 48 -------->equation 1.

Father's age was five times the age of the son.
Son age x;
Father age 5x;
x = 5x.
Son age and father age substitute in equation 1.
Son + father = 48.
x + 5x = 48.
6x = 48.
x = 8 (x = 5x).

The present age of son:
Six years ago the age of son+6.
8 + 6 = 14.

After 6 years, son's age will be:
Son present age +6.
14 + 6 = 20.

@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

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.

Thank you everyone for explaining the solution.

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.

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/.

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.

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/.

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.

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?