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.

@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.

Very helpful. Thanks for explaining @Amit.

Thanks @Amit.

@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.

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.

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.

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 .

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.