Aptitude - Problems on Ages - Discussion

If father's present age is x and how we have to treat x + 3 or 3x in the question?

They mention like son age is 3 times than father age in 3 years hence.

10 years ago:

Son = x - 10,

Father = 3 (x - 10).

10 years hence:

Son = x + 10.

Father = 2 (x + 10).

Equating the age of the father at hence 10 years, so we have to add 20 in the past 10 years.

So,

3 (x - 10) + 20 = 2 (x + 10),

3x - 30 + 20 = 2x + 20,

3x - 2x = 30 - 20 + 20,

X = 30.

Now for present ratio, we will add 10 to past equation.

So,

3 (x - 10) + 10 : x - 10 + 10,

3 (30 - 10) +10 : 30 - 10 + 10,

3 (20) + 10 : 30 = 70 : 30,

7 : 3.

10 years ago,
Father age is = (3x - 10).
Son age = x.

10 years now.

Father age = 3x - 10 + 10 -------> (2).
Son age is 2 (x + 10) = 2x + 20 -------> (1).

1 = 2.

3x - 10 + 10 = 2x + 20.
x = 20.

What is the meaning of fathers age will be twice that of his son?
2(3x + 10 + 10) = (x + 10 + 10).

Why are you taking?
(3x + 10 + 10) = 2((x + 10) + 10).

Please tell me.

I need an answer to this question and way of solving.

The present age of the father is four times of his son. When will the son be as old as a father now their ages will be 99 find their present ages?

In all these questions, we simply assuming son's age as x and father 's age as nx (n=number given).

And why in this question alone we are assuming son's age as x and father 's age as y.

Pleas say the difference.

Hi.

Let as consider
Father's age = x.
Son's age = y.

=> 10 year Ago Father's age is x - 10 = 3(y-10) -----> Equation 1.
=> After 10 years Father's age x + 10 = 2(y+10) ------> Equation 2.

Solve 2 equation......
=> x - 10 = 3y - 30.
x - 3y = - 20 --> Equation 3.
=> x - 2y = 10 --> New Equation 4.
=> Substract Equation 3 from Equation 4.
x - 3y = - 20
x - 2y = 10
----------------
- y = - 30.

So, y = 30 --> age of son.

Then put y =30 into any equation.

x - 2(30) = 10
x - 60 = 10.
x = 70 --> age of father.

x = 7.
y = 3.

I hope, this will help you.

Let's present ages of father and son will be x and y.
Before 10 yearss, it will be (x - 10) = 3(y - 10).

Ten years hence , the equation will be x + 10 = 2(y + 10).
Solve these two equations, we get x = 70 years and y =30 years.

The age of the son and the father are in the ratio 3:10. If the father have 52 years, how old is the son?

@Arshad.

We can calculate from present age either hence or later and also ago, before, after in any age problems.