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.

@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.

It doesn't make sense why ppl take the fathers age as 4X just becos its says 'times more' . what if the son's age is 'times less' of the father? :D

So I made a calculation based on logic and it comes to this
son's age = x.
Father's age = X x 3 = 3X.

After 8 years father is 2 and half years older than his son, so if we add 8 years to the fathers age it will be equal to 2 and a half times of the son's age.

i.e 3X + 8 = 2 and a half times of X.
3X + 8 = 2 1/2 x X.

From the equation X = 16.

Now the fathers initial age = 3X.
= 3 x 16 (X=16).
= 52.

After 16 years (8+8 years) father will be,
= 52 + 16.
= 64.

In the same way the son after 16 years will be,
= X + 16.
= 16 + 16 = 32.

Hence the difference of their age will be, 64 divided by 32
= 64 / 32.
= 2.

So the Father will be 2 times older than the son in 16 years :D.

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.

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.

Hi frndz my solution takes much lenghthy, but have tried to give a clear explanation

Let Father=F & Rohith=R
consider R's age as "X"
Now F's age will three times morethan R's age, so it'll be X+3X=4X
Now in 2011 F's age is 4X and R's age is X, but after 8 years say 2019 what is the F's age?
4X+8 and R's age X+8 (add 8 to F' and R)
As mentioned in the statement the age of F's is two and half(2+1/2) times ,so it will be 5/2.

STEP1:
Now on LHS side it is F's age
4X+8
and RHs it is R's age X+8 multiple of 5/2 as
4X+8=x+8(5/2)
=> 2(4X+8)=5(X+8)
=> 8X+16=5X+40
=> 8X-5X=40-16
=> 3X=24
=> X=24/3
Therefore X=8

STEP2:
again after 8 years
(4X+8+8)=(X+8+8)
=>4x+16=x+16
=>4x+16/x+16=?
we have X=8

So,
4*8+16/8+16=?
32+16/24=?
48/24=?
the ans is "2"

Hope u got it..

Hi friends,

Let son"s age is =1 then father age=4
which means ratio between father to son= 4 :1 (say f: s)........[1]
after 8 years this ratio = 2.5 : 1 ( f :s)
= 5:2...................[2]

but one thing is clear that difference betwwen father age and son age will always be same.


In eq. [1] difference is 3 and in [2] is 3 as it shuld be.

Now take a look at fther age .............it was 4 and after 8 years it is 5 ...it means in our values
I
n the ratio 1=8,
so ........................5=40(father age after 8 years)
and.......................2=16(son age after 8 years )

Hence after further 8 years later father age =40+8 =48 years and
................. son age = 16+8= 24

So ratio = 48:24
=2:1

Let the present age of Rohit be 'x' years and the present age of the father be 'y' years. As per the question father is aged three times more than his son hence, y = x+3x = 4x.

Therefore present age of father is y = 4x.

Given that after 8 years, he would be two and half times of Rohit's age.

Therefore,

y+8 = 5/2(x+8).
4x+8 = 5/2(x+8) {since y = 4x}.
2(4x+8) = 5(x+8).
8x+16 = 5x+40.
8x-5x+16-40 = 0.
3x-24 = 0 => 3x = 24 => x = 24/3 = 8.
x=8,

After 8 years,

y+8 = x+8.
4x+8 = x+8 {since y = 4x}.

After further 8 years, 'k' times would be the Rohit's age.

Therefore,

4x+8+8 = k (x+8+8).
4x+16 = k (x+16).
k = (4x+16) / (x+16).
k = (4.8+16) / (8+16).
k = 48/24.
k = 2.

Therefore 2 times would he be Rohit's age.

I think answer is 2.2 times.

x = son Ronit's age now.

3x = father's age now <--- father is 3 times son.

x + 8 = Ronit's age in 8 years.

3x + 8 = father's age in 8 years.

3x + 8 = 2.5 (x + 8) <--- after 8 years, father is 2.5 times son.

3x + 8 = 2.5x + 20 <--- used distributive property.

0.5x = 12 <--- subtracted 2.5x and 8 from each side.

x = 24 <--- divided each side by 0.5.

3x = 72 <--- substituted 24, in for x, into 3x.

Son Ronit is 24 now & father is 72 now.

Son Ronit will be 32 in 8 years & father will be 80 in 8 years.

Son Ronit will be 40 after further 8 years & father will be 88 after further 8 years.

Father will be 2.2 times son after further 8 years.

Let Ronit's age = x.

So father's age will be (x+3x), (Let suppose you have sister who is 1 year younger than you then after 20 year your age will be 21 (Your sister age + 20 yr) = your age. So same in this question father age will be x+3x.

Now after 8 years mean rule no.2 (If x is current age then n year later age will be (x+n)).

Father's age will be (4x+8) and Ronit's age will be (x+8).

Now come to question that after 8 years father's age will be 5/2 times of Ronit's age.

So F age = 5/2 times of Ronit's age.

4x+8 = 5/2(x+8).

So by this we get x = 8.

Now we have to find after 8 year.

= 4x+8+8 = y(x+8+8).

So by solving this y = 2.

Thank you :).