Aptitude - Problems on Ages - Discussion

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.

@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

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.

Consider son present age is X and father present age is Y.

X + Y = 60 consider this is first equation,

6 year ago father age is,
(Y - 6) = 5(X - 6),
5(X - 6) = Y - 6,
5X - Y = 24 this is second equation.

After solving 1 and 2 equation,
X = 14,
After 6 year son age is 14 + 6 = 20.

Thank you @AMIT.

Age of the son 6 years ago = 'X'.
Age of the father 6 years ago = '5X'.

At present sum of the father and son's age = (X + 6) + (5X + 6) = 60.
=> X = 8 which is assumed as the age of 6 years ago so, at present age of the son is X + 6 i.e 8 + 6 = 14.

After 6 years age of the son 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 the ratio of father and son 6 years ago was 5x:x.
Both father and son age's sum 6 years ago was,
60-12=48,
Then, 5x+x=48,
6x=48,
x=8.
Father age was 5*8=40 and son's age was 8.
At present father age is 40+6=46 and son's age is 8+6=14.
At present father and son's age some 46+14=60.
Then how the son's age is 20?

Present age of F+S=60.
F=60-S.
6 years ago age of F+S=60-6-6=48-----(1)
and 6years ago son age is (s-6) and father age is 5(s-6).
Substitute these are in eq(1).
5(s-6)+(s-6)=48,
5s-6s+s-6=48,
Present age of son is S=14.
From F=60-s,
=>F=60-14,
Present age of father F=46.

After 6years son age is S=14+6
S=20 years.
After 6 years father age is F =46+6=52.

The age of A and B three years ago were 'x' and 'y+2' years, therefore the sum of their ages 4 years hence will be?

Can someone solve this?