# Aptitude - Problems on Ages - Discussion

Discussion Forum : Problems on Ages - General Questions (Q.No. 8)
8.
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
12 years
14 years
18 years
20 years
Explanation:

Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 - x) - 6 = 5(x - 6)

54 - x = 5x - 30

6x = 84

x = 14.

Son's age after 6 years = (x+ 6) = 20 years..

Discussion:
69 comments Page 1 of 7.

Veera said:   5 months ago
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 .
(1)

Arshpreet Kaur said:   12 months ago
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.
(8)

Hiwote end said:   2 years ago
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.
(37)

Mahendran Kamaraj said:   3 years ago
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.
(27)

Rituparna Pati said:   3 years ago
@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.
(6)

M Mahd Pakistan said:   4 years ago
Thanks @Amit.
(3)

Hassan said:   4 years ago
Very helpful. Thanks for explaining @Amit.
(1)

Abhi said:   4 years ago
@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.

(2)

Nikhil G said:   4 years ago
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.
(1)

Isha said:   4 years ago
Very easy to understand, Thanks @Amit.
(2)