Aptitude - Problems on Ages - Discussion

I'm confused with this answer. I solve like this correct me if I'm wrong.

Let the present age of father = x.

Let the present age of son = y.

Sum of present age: x+y= 60 then equate will become: y = 60-x.

6 years ago the age of father will be 5 times the age of his son.

Father: x-6.
Son: y-6.

Equate these 2 equation, would become:

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

By substituting the value y = 60-x:

x-6 = 5(60-x)-30.

x = 46 (present age of father).

Substitute the age of father to y = 60-x would gives us the present age of his son.

y = 60-46.

y = 14 (present age his son).

14 is my answer;

Thank you!

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 .

Sum of present ages of a father and his son is 60 years.
Son + Father = 60

Six years ago:

Son + father = 60 - 12( six years ago means son-6 and father-6 )
Son + father = 48 -------->equation 1.

Father's age was five times the age of the son.
Son age x;
Father age 5x;
x = 5x.
Son age and father age substitute in equation 1.
Son + father = 48.
x + 5x = 48.
6x = 48.
x = 8 (x = 5x).

The present age of son:
Six years ago the age of son+6.
8 + 6 = 14.

After 6 years, son's age will be:
Son present age +6.
14 + 6 = 20.

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.

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.

@All.

Let father & son's age be x&y.

As said present sum of x + y = 60.

& six yrs ago father's age was five times the age of his son i. e
(x-6) = 5(y-6)>>>eq 1.

x + y = 60>>we can ryt this as x = 60 - y.
So, substitute x value in eq 1.

(60 - y - 6) = 5(y - 6)
54 - y = 5y - 30
54 + 30 = 5y + y
84 = 6y.
So,
y = 84/6 = 14,
y = 14.
And y's age after 6 yrs =(y + 6).
= 14 + 6 = 20yrs.
So answer is D

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.

The sum of son and father's age can be written as
S+F=60 ----------(1)
before 6 years ago
5(S-6)=F-6
5S-30=F-6
5S-F=-6+30
5S-F=24 ----------(2)
ADDING (1) and (2),weget
6S=84
S=84/6=14
put s=14 in ist weget
F=46

Hence after 6 years Son;s age will be 14+6=20 years.

Father = 60-x.
6 years ago so (-) symbol if it is after 6 years means we add (+) symbol.

We add 6 to both sides,
(60-x)-6 = (x-6).

Here ques asked father's age was five times the age of the son

So,
(60-x)-6 = five times of(x-6) /(x-6) is sons age)/.
(60-x)-6 = 5(x-6).
54-x = 5x-30.
6x = 84.
x = 84/6.
x = 14.

After 6 years, son's age will be:
Son age x.
After six years so;
x+6.
14+6 = /20 years/.

Let father's age = X.

Let son's age = Y.

So, A/Q X+Y = 60 (Equation 1).

But six years ago father's age was five times the age of the son.

So, X-6 = 5(Y-6) (Equation 2).

Now putting the value of X = 60-Y from (Equation 1) in (Equation 2).

So, 60-Y-6 = 5(Y-6).

So the value of Y = 14.

But in question we have to find the son's age after 6 years so added 6 in 14. So, answer will be 20 years.

FINE!