Aptitude - Problems on Ages - Discussion

Sum of both ages is F + S = 60

We can also write as F = 60 - S ------> Eqn 1.

6 years ago father age will be 5 times the age of son -> eq becomes F - 6 = 5 (S - 6)------> Eqn(2).

Then substitute eq(1) to eq(2).

Then eq becomes (60-S)-6 = 5 (S - 6).
(60-S)-6 = 5S - 30,
60+30-6=5S+S,
84=6S,
S = 14.
Then add 6 to it (because after 6 years so)so 14 + 6 = 20.

@Amit.

You have already added 6 to bring question in present (x+6) & (5x+6). Now the outcome of this solution is 8yr right. This 8yr must be present age of son we have to add 6 to know future age hence, 8+6=14.

How have you added 8+6+6? I didn't understand please reply.

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.

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.

x+y = 60 -------------> eqn1
5x-6 = y-6 => 5x = y ----------> eqn2

Equating both equation:
y/5 = 60-y.
y=300-20y.
y=300/19.
y = 14 years.

After 6 years 14+6 = 20.

Very helpful. Thanks for explaining @Amit.

6 years ago son age = x, then father = 5x.

Present age of son means x+6 like that father age is 5x+6.

x+6+5x+6 = 60. So x = 8, here it is.

After 6 years son age will be x+6+6 = 8+6+6 = 20.

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.

Thank you @AMIT.

Consider son present age is X and father present age is Y.

X + Y = 60 consider this is first equation,

6 year ago father age is,
(Y - 6) = 5(X - 6),
5(X - 6) = Y - 6,
5X - Y = 24 this is second equation.

After solving 1 and 2 equation,
X = 14,
After 6 year son age is 14 + 6 = 20.