Aptitude - Problems on Ages - Discussion

@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.

The given answer is Incorrect, below is the right answer with a detailed explanation.

let's denote the son's current age as R and the father's current age as F.

Step 1: Setting up equations
From the problem: The father is three times older than the son.
F=3R
After 8 years, the father will be two and a half times older than Ronit. After 8 years, the father's age will be
F+8 and Ronit's age will be
R+8. According to the problem, after 8 years:
F+8=2.5(R+8)
Step 2: Solve the system of equations
From the first equation, substitute
F=3R into the second equation:
3R+8=2.5(R+8)
Simplifying the equation:
3R+8=2.5R+20
Now, subtract
2.5R from both sides:
0.5R+8=20
Subtract 8 from both sides:
0.5R=12
Now, divide by 0.5:
R=24
So, Ronit's current age is
R=24.

Finding the father's age:
Since
F=3R, we substitute
R=24:
F=3×24=72
So, the father's current age is
F=72.

Step 3: After 16 years
After 8 more years, the father's age will be
F+16 and Ronit's age will be
R+16.
The father's age after 16 years is:
F+16=72+16=88
Ronit's age after 16 years is:
R+16=24+16=40
Now, the question asks how many times the father's age will be compared to Ronit's age after further 8 years (16 years in total). So, the ratio of the father's age to Ronit's age after 16 years is:

88/40 =2.2

Thus, after 16 years, the father will be 2.2 times as old as Ronit.

Present age ratio F:S = 1:4
After 8 years(2.5:1) = 5:2.
1p = 8 years
5p = 40 years 2p =16.
Another 8 years later. 48:24 = 2:1.

How came 5/2? Please explain to me.

It's 16 because we assume the son's age is x and the father is x + 3x = 4x.
We equate it and find the son's present age is 8.
So, we need to find 8+8 years, that's how it became 16.