Aptitude - Problems on Ages - Discussion

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.

How come 16 here? Anyone, Explain to me.

@All.

This question is a tricky one, as it states Father's age is three times more than Ronit's age. The "times" would imply F=3R but it also has a "more" statement. Meaning that Father's age is what adds to 3 times Ronit's age to Ronit's age, which means.

F = 3R+R.

How it's 16 years? Can anyone please explain?

How ratio be calculated in this question? Please explain to me.

Let son age = x.
Father age = y.

X + 3x = y( acc to 1st statemnt) ---> eq1
5/2(X+8) = y+8.
5x+40 = 2y+16.
5x-2y=-24 ---> eq2.

Solve eq 1 and 2 we get;
X=8 then y = 24,
After 16 years,
Son age 24 & father age 48.
Therefore 2 times.

In the question, son's age is 2 (1/2) age.

So, 2x1/2 is 5/2fraction form.