Aptitude - Problems on Ages - Discussion

f+s = 60.
f-6 = 5(s-6),
f = 5s-30 +6,
f = 5s-24,
f+s = 60,
5s-24+s = 60,
6s=60+24 = 84,
s = 14 but our target to find son age after 6 years. 14+6= 20.

Son's age= x,
Father's age is y.

x+y=60 -------> (1).
As per 2nd statement;
(y-6) = 5(x-6).


5x-y=24 ------> (2).

Therefore solving equ. 1 & 2.
x=14 & y = 46.

3rd condition;

Son age after 6 years.
14+6= 20 years.

Let the father's age be x years and son's age be y years.
x + y = 60-->eqn 1
6 years ago.
x - 6 = 5(y-6)
x - 5y = -24--> eqn 2

By solving equations 1 and 2, we get
y = 14.

Son's age after 6 years = 14 + 6,
= 20 years.

F + s = 60.
Before 6 yrs— f+s = 60-12= 48
F. : s
-6yrs = 5. : 1
+6yrs = ?

5x + 1x = 48,
6x = 48,
X = 8.
12 yrs. = total time difference.
Hence, the son is 1 part => 1*8 = 8.
After 12 yrs, son = 8+12= 20 years.

Hello friends.

In this question, they give the sum of the present age of father and son but they don't give both of real age. So, first, we assume father and son's ages as,
Father = X,
Son = Y.

First step: (Present)
The Sum of father and son's present age is,
X+Y=60 -> (1)
6 years ago (past) /here in the past we use (-)
Son = X-6, Father = Y-6.
Father's age was 5 times the age of the son so,
Now,
X-6 = 5(Y-6) -> (2)
(1)÷-(2).
{X+Y = 60
-X+5y = 24}
Therefore, Y = 14.

After 6 years son's age will be is,
14 +6 = 20 .

@Amit.

You have already added 6 to the years to convey the present years of both of them. Then why have you added another 6 years. I can't understand! Please explain it.

Thanks @Amit.

Very easy to understand, Thanks @Amit.

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.

Hey amit you already added 6 initially,
(x+6)+(5x+6)=60
x+5x+12=60
6x+12=60
6x=60-12
6x=48
x=8 and at end we haveto add another 6 means 8+6=14 years ....then how it would be 20 so actual answer is also wrong