Aptitude - Problems on Ages - Discussion

Answer is D i.e. difference between age of R and Q is 12.5 years.

Explanation: lets take age of T is x (youngest among all of three) and accordingly age of Q is 2x and age of R is 3x. (from the very first sentence of question we come to know that there is exact age difference between Q and R and Q and T where R is elder one Q is middle one and T is younger hence age of T if taken as x then age of Q becomes 2x and age of R becomes 3x)

we can hence say that,
x+2x+3x = 50(i.e. sum of ages of R and T) + 2x (age of Q)

x+2x+3x = 50+2x,
x+2x+3x-2x = 50,
4x = 50,
x = 12.5.

Hence, age of T = 12.5.
and accordingly, age of Q = 25 (2*12.5) and age of R = 37.5 (3*12.5).

Hence, difference between age of R and Q = 37.5-25 = 12.5.
The option is not given hence data is inadequate.

Even, I did it wrong at first instance. Although, I am quite elderly age - 32 years.

The problem here is that you are assuming the age to be,

3x 2x and x of R,Q, and T respectively.

However, there can be multiple such assumptions -- for example:

6x, 4x, and 2x. -- multiple of 2.
9x, 6x, and 3x ---- multiple of 3.
.....
and so on. So, you cannot have a definite answer. See the difference will be x for the first case.
The difference will be 2x for the second case.
The difference will be 3x for the third case.

The difference will be nx for the nth case.

So, the definite difference cannot be determined. however, you can determine the ratio of their ages, which is constant - 3:2:1.

Hello People,

We all Know that Q is 25.

The question to find out the "DEFINITE" difference between the age of R and T.

Given is that the difference between the ages of T and Q = R and Q.

The sum of ages of R and T = 50.

So if Q is 25 then.

T = Q - 1 hence R = Q + 1.

T = 25 - 1 hence R = 25 + 1.

T = 25 - 2 hence R = 25 + 2.

T = 25 - 3 hence R = 25 + 3.

T = 25 - 4 hence R = 25 + 4.

T = 25 - 5 hence R = 25 + 5.

T = 25 - 6 hence R = 25 + 6.
.
.
.
T = 25 - 24 hence R = 25 + 14.

Hence it will be impossible to "definitely" ascertain the ages of T and R.

Hence the option D) Data is inadequate.

As per the first line of question, Q and T are of the same age. It just indicated relation with T in terms of showing R as older than T and Q is younger than R. Which means both Q and T are younger than R and it's not possible the way all r considering it like Q and T are of different age. That's why it indicates the same as T which is both Q and T are of the same age. Just take a note and write down the relationship of R and Q separately. N also try to compare with the condition.. u won't get Q and T as different ages. Because they are the same. The info we have is

R+T=50 and R-T = R-Q.

The eldest is R. Then second is Q. The youngest is T.

But it is said Q is MUCH YOUNGER THAN R. So if we consider the answer A it is 1 years, that answer will not come because it is said that Q IS MUCH YOUNGER THAN R.

Similarly answer B too will not come. Similar reason.
But if we consider about answer C it is said 25 years.

It also will not come because, R IS OLDER THAN Q.

SO IF R IS 50 YEARS THEN Q MUST TO BE 25 YEARS.

BECAUSE THEN ONLY THE DIFFERENCE WILL BE 25 YEARS. BUT IT WON'T HAPPEN.

AS IT IS SAID R+T=50..So T will n't be equal to zero. UNDERSTAND GUYS?

From above question:

Given,
R - Q = Q - T ------> 1st condition
R + T = 50 ------> 2nd condition
With this, we can find Q,
R - Q = Q - T.
R + T = 2Q,
2Q = 50,
Q = 25.

With the help of condition 1,

We know that the difference between R and Q,Q and T were same, consider it as 'x'. i.e., T=Q-x, R=Q+x.

Now consider T=1 year,
Then the difference between Q and T is (25-1)years i.e., x=24 years.
Then R =Q+x= 25+24= 49 years.

Check it satisfies both of the conditions.
R + T = 50.
R - Q = Q-T.

Now the difference between R and Q is (49-25).
= 24 years.

From above question:

Given,
R-Q = Q - T -------> 1st condition
R+T = 50 -------> 2nd condition.
With this, we can find Q,
R-Q = Q-T
R+T = 2Q
2Q = 50
Q = 25.

with the help of condition 1,

We know that the difference between R and Q,Q and T were the same, consider it as 'x'. i.e., T=Q-x, R=Q+x.

Now consider T=1 year,
Then the difference between Q and T is (25-1)years i.e., x=24 years.
Then R = Q + x= 25 + 24 = 49 years.

Check it satisfies both of the conditions.......
R+T=50
R-Q=Q-T

Now the difference between R and Q is (49-25)
= 24 years

I think (E) will be the answer..........
because:
If we let, as per question, the age of T = x
then, Q must be 2x and R must be 3x.
From the question we also get, R+T=50
Now, we have to find R-Q=?
As R+T=50
or, 3x+x=50
or, 4x=50
or, x=50/4
Therefore, the age of R = 3x
= 3 * 50/4
= 37.5
and the age of Q = 2x
=2 * 50/4
=25
Therefore, R - Q = 37.5 - 25 = 12.5 (Answer:E)

Here I have done a reverse method to find answer.

So according to question T is the youngest one then Q and then R.
So if we consider T = x.

And try options in it.
First ans is 1 year difference, if this is right then Q=x+1 and R = x+2

Question says,
T+R = 50.
x+x+2= 50.
x= 24.
x=T.

Therefore, T= 24years.
Q=25.
R=26.

Then this fulfil both the criteria of age difference as well as the sum total of R and T.
Therefore option A: year is right.

Let the age of 'Q' be x.

As R is older than Q we can assume 'R' be x+1.

And T is the same year younger than Q as R is older than Q, we assume 'R' is x-1.

The sum of R and T = 50 (given).

Then,

=> (x+1) + (x-1) = 50.
=> 2x = 50.
=> x = 25 years (age of Q).

Hence,

=> x+1 = 26 years.
=> x-1 = 24 years.

Difference between R and T is 2 years.

(Instead of what difference we can also take 2 years means (x+2) + (x-2) or any number like this.)