Aptitude - Problems on Ages - Discussion

@All.

The correct answer is B.

Here is the explanation for the solution:

Let's first represent Ronit's current age as "R" and Father's current age as "F."

According to the information provided:

1. Father's age is three times more than Ronit's age: F = 3R
2. After 8 years, Father's age would be two and a half times Ronit's age: F + 8 = 2.5 * (R + 8)

Now, let's solve the equations to find the current ages of Ronit and his Father:

From equation 1, we have F = 3R
Substitute this value of F in equation 2:
3R + 8 = 2.5 * (R + 8)
Now, let's solve for R:
3R + 8 = 2.5R + 20,
3R - 2.5R = 20 - 8
0.5R = 12,
R = 12/0.5.
R = 24.

Now that we know Ronit's current age (R = 24), we can find Father's current age using equation 1:
F = 3R.
F = 3 * 24.
F = 72.
After further 8 years, Ronit's age will be:
Ronit's age after 8 years = R + 8 = 24 + 8 = 32.

Father's age after 8 years will be:
Father's age after 8 years = F + 8 = 72 + 8 = 80.

Now, let's find out how many times Father's age will be of Ronit's age after further 8 years:
(Father's age after further 8 years)/(Ronit's age after further 8 years) = 80/32 = 2.5.
After a further 8 years, Father's age will be 2.5 times Ronit's age.

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.

Father aged 3 times more than his son Ronit", everyone would think Father's age is triple of Son's age, right?

How to assume this? Anyone, please explain me clearly.

@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.

Let's assume the current age of Ronit is R years. According to the problem, the father's age is three times that of Ronit's age.

Therefore, the current age of the father is 3R years.

After 8 years, Ronit's age will be R + 8 years, and the father's age will be 3R + 8 years.

According to the problem, the father's age will be two and a half times Ronit's age at that time. we can write:

3R + 8 = 2.5(R + 8).

Let's solve this equation to find Ronit's current age:

3R + 8 = 2.5R + 20.
0.5R = 12,
R = 24.

Therefore, Ronit's current age is 24 years. Consequently, the father's current age is 3R = 3 * 24 = 72 years.
After another 8 years, Ronit's age will be 24 + 8 = 32 years, and the father's age will be 72 + 8 = 80 years.
To find out how many times the father's age is of Ronit's age at that time, we divide the father's age by Ronit's age:
80/32 = 2.5
Therefore, after a further 8 years, the father will be 2.5 times Ronit's age.

At present, F and R.

R=R,

Father's age would 3 times more than Ronit's age
F=3R+R -> F=4R -----> (1)

After 8 years, F+8 and R+8.

Father would be 2 and half a times of Ronit's age
F+8=2 1/2(R+8).

Mixed fraction 2 1/2 = ((2*2)+1)/2 = 5/2.
F + 8=5/2(R+8),
2F+16 = 5R + 40,
2F-5R = 40 - 16,
2F-5R = 24 -------> (2)

Sub F=4R in (2).
2(4R)-5R = 24,
8R-5R = 24,
3R= 24.
R = 8 years, F = 32 years.
After further 8 years means;
F + 16 = 32 + 16= 48,
R + 16 = 8 + 16= 24,
Required ratio= 48/24 = 2.
Hence, After further 8 years, 2 times he would be of Ronit's age.

As someone has doubts on 5/2.

As it is mentioned in the question, the father would be (two and a half time's) Ronit's age.
So, it is in the form of a mixed fraction.
We write one and a half is 1/2
So 2 and a half is = 2 1/2,
So, 2*2+1/2,
= 5/2.

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.

@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.

Why 5/2 is used? Please explain to me.