Aptitude - Problems on Ages - Discussion

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.

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.

6 years ago son age = x, then father = 5x.

Present age of son means x+6 like that father age is 5x+6.

x+6+5x+6 = 60. So x = 8, here it is.

After 6 years son age will be x+6+6 = 8+6+6 = 20.

Father age = f, son age = s.

Then f+s = 60;

f+6 = 5(s+6).

On solving s = 6;

Then present age of son = s+6 = 6+6 = 12;

Then after 6 years it will be = 12+6 = 18;

What is wrong in that?

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!

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!

Son = x.
Father = y.

Then, x+y = 60.....(1).

6 years ago.

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

That is y-6 = 5x-30.

Therefore at present age we have y-6+6 = 5x-30+6.

That is, y = 5x-24.

From (1).

x+5x-24 = 60.
6x = 84.
x = 14.

Therefore after 6 years sons age will be.

14+6 = 20.