Aptitude - Problems on Ages - Discussion

We can solve like this also:

Father is mentioned as 'f'.
Son is mentioned as 's'.

Sum of father and son age ==> f+s = 60 ----- (1).

Before 6 years ==> (f-6) = 5(s-6).

F-5s = -24 -------------- (2).

Solve equation 1 and 2 we can get the value of s = 14.

The current age of son is ===> 14.
After 6 year ==> 14+6 = 20.

Present age of son = x.
Present age of father = 5x.

6 years ago.

Son's age = x + 6.
Father's age = 5x + 6.

Sum of their ages.

X+6+5x+6 = 60.
6x = 48.
X = 8.

Son's age = x+6 = 14.

After Six Year's
14+6 = 20.

Hence 20 is correct answer.

Take father age = x.
Son age = y.

Sum of father+son = 60.
x+y = 60 eq(i).

6 yrs ago father age is 5 times the age of son.

x-6 = 5(y-6).
x-6 = 5y-30.
x = 5y-30+6.
x = 5y-24.

Sub x value in eq(i).
5y-24+y = 60.
6y = 60+24 = 84.
y = 14.

Then 6 yrs after the son age = 14+6 = 20 years.

Let the present age of the father is F, Son's present age is S.

The sum of their ages S + F = 60.

Fathers age 6 years ago (means - 6) F - 6,

Sons age 6 years ago S - 6,

Now given Six years ago, father's age was five times the age of the son.

Six years ago, father's age: F - 6 = 5(S - 6),

F - 6 = 5(S - 6) ---> Eq1

F + S = 60 ---> Eq2

by solving we get S = 14.

Question is to find after(ADD) 6 years so ADD 6.

Hence, Sons's age after six years will be 20 years.

Fathers age 4 times of his son means.

Sons age X.
Fathers age 4x.

Or

Sons age 4x.
Fathers age x.

Which one is right ? How to solve explain ?

@Priya.

Your logic is correct but you have to subtract 12 from 60. You have subtracted 6 for sons age and for fathers age you have to subtract another 6 know so it will be 60-12 = 48 not 54.

If you want me to explain precisely means please let me know.

s=x
f=y
x+y=60......................(1)
6 years ago
(y-6)=5(x-6)
i.e
y-6=5x-30
Therefore at present age we have
y-6+6=5x-30+6
i.e
y=5x-24

From (1)
x+5x-24=60
6x=84
x=14

Therefore after 6 yrs sons age will be
14+6=20

Let 'F' be the Father's Age and 'S' be the Son's Age.

According to situation:

F+S = 60 EQ ---- 1
F-6 = 5(S-6) ,
Which is F-6 = 5S-30 EQ ---- 2

F = 5S -24 EQ ---- 3
Put this in EQ 1

5S - 24 + S = 60
6S = 84
S = 14

After 6 Years Sons age will be S = 14 + 6 = 20

@Amit thanks yar. Your method is easy and simple to understand :).

Now son age x and father age is y
then
x+y=60---->1
six years before son=x-6, father=5(x-6)
so
y-6=5(x-6)
y-6=5x-30
5x-y=24--->2
solve 1 and
get x=14
x is present age
after six years x+6=20