Aptitude - Problems on Ages - Discussion

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 easy to understand, Thanks @Amit.

Thanks @Amit.

Thank you all.

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.

My solution is given by,
The present sum of ages 60.
So 6 years ago the sum is 48.
Then the ratio is 5:1 it means 5x+x=6x=48.
Then x=8 and,
Age after 6 years is 40+12=52 and 8+12= 20.

Here, in this question, we can see 3 periods of time(past, present, future).
Take past first, ie, 6 yrs b4:

son=X and dad=5X.

Now take present:

Son=X+6 and Dad=5X+6.

Given a hint that at present their sum of ages is 60; a task made easy.

X + 6 + 5X + 6 = 60,
X = 8.

Now take future (we have to find ans in future):

After 6 more yrs:
Son=X+12 and dad=5X+12
So the son will be 8+12 yrs old.

The age of son =20.

Let father age be x.
Son be y.

X+y=60,
X-6=5y,
Y=x-6/5.

Sub y in above eq.
X+x-6/5=60.
5x+x-6=300.
6x=294.
X=49 father age.
Sub x in above.
49+y=60.
Y=11.
After 6 years 11+6=17 years.

Thank you so much for explaining the answer.

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.