Aptitude - Problems on Ages - Discussion

How to add 8 more in a 16 ratio?

Very clear, thanks all for explaining the answer.

Present ages F : S = 4:1(because father is 3 times more than son which is 4-1 =3)
Father = 4R.
Son = R.

After 8 years
F: S = 2.5 : 1.

(4R + 8)(R+8) = 2.5
4R + 8 = 2.5(R + 8),
4R + 8 = 2.5R + 20,
4R - 2.5R = 20 - 8.
1.5R = 12.
R=12/1.5 = 8.
If R is 8 then 4R is 4(8)= 32, that is, father's age after 8 years.
So, after 16(that is, after 8 years + after 8 years).
F = 32 + 16 = 48.
S = 8 + 16 = 24.
F:S = 48:24 = 2:1.
That is Father's age 2 times more than son after another 8 years.

4x + 8 = 2.5x + 20.
1.5x = 12,
x = 12/1.5
x = 8.
24/48 = 1/2.

@All.
Simply;
Ronith's present age = x.
Father's age=3 times more than Ronith's age.
So, x + 3x = 4x.
So, after 8 years, 4x + 8 = 5/2(x+8) by doing the calculation we will x = 8.
Further 8 years:
Now we are in the present stage, so they have asked for a further 8 years,
So, a further 8 years and an additional 8 years =16 years.
=> 4x + 16/x + 16+2.

@All.

My doubt is; in the question, it is given "Father has aged 3times the son" then how father's age will be x + 3x = 4x? If 4x is father age then it will become wrong. right?

Ex. Let son age be 2 years, father age will be 8years (4x, as given in explanation). Then how it will be correct?

Anyone, explain this to me.

He would be 2 (1/2) times of Ronit's age.

2 1/2 which is a mixed fraction. So it is written as [ (2*2) +1]/2 = 5/2.

Ronith's present age = x.
Father's age=3 times more of Ronith's age.
So, x + 3x = 4x.
So, after 8 years, 4x + 8 = 5/2(x+8) by doing the calculation we will x = 8.
Further 8 years: Now we are in the present stage, so they have asked for a further 8 years, so future 8 years and a further 8 years =16 years.
=> 4x + 16/x + 16+2.

Here is how 5:2 comes;

Initially it was 2.5:1.
To remove the decimal point,we need to multiply by 10 in the numerator and denominator also.
= 2.5/1 x10/10.
= 25/10 (on cancellation with 5, it becomes),
= 5:2.

The correct answer is

Let's solve this step by step:

Step 1: Define the variables
Let Ronit's current age be (x).
Let the father's current age be ( 3x ) (since the father is three times older than Ronit's age).

Step 2: Form an equation for the first condition
After 8 years:
- Ronit's age will be (x + 8).
- Father's age will be ( 3x + 8).

The problem states that the father would then be two and a half times (2.5 times) Ronit's age.

[3x + 8 = 2.5(x + 8)]

Simplify this equation:
3x + 8 = 2.5x + 20
3x - 2.5x = 20 - 8
0.5x = 12
x = 24.

So, Ronit's current age is ( 24 ) years, and the father's current age is (3x = 72) years.

Step 3: Calculate their ages after a further 8 years.
After 8 more years (16 years from now):
- Ronit's age will be ( 24 + 16 = 40).
- Father's age will be ( 72 + 16 = 88).

Step 4: Find the ratio of their ages.
The ratio of the father's age to Ronit's age after 16 years is:
Father's Age Ronit's Age = {88}{40} = 2.2

Final Answer:
After 16 years, the father will be 2.2 times Ronit's age.