Aptitude - Problems on Ages - Discussion

14. 

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

[A]. 1 year
[B]. 2 years
[C]. 25 years
[D]. Data inadequate
[E]. None of these

Answer: Option D

Explanation:

Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined.

Pragna said: (Jul 5, 2010)  
Can you explain breifly pls?

Wgn said: (Jul 9, 2011)  
As it is mentioned that, what is definitely the difference between R and Q's age? So we need to get the exact difference.

Now, answers could be
1)10 and 40 with a difference of 30(40-10)
2)20 and 30 with a difference of 10(30-20)

So, as we can have more than 1 answers, so the definite difference cannot be calculated.

Therefore, the data is inadequate. Ans: D

Niladri Shekhor Hira said: (Feb 13, 2012)  
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)

Shweta S said: (Feb 17, 2012)  
It cant be E coz they just mentioned younger and older not the figure like 3 year or 2 years younger... So it cant be E

Deepak Varshney said: (Mar 25, 2012)  
Let X be the age of Q and Y be the number of years that R and T is older and younger than Q.(as per question)

Therefore the age of R and T be X+Y and X-Y
and we know that R's age +T's age =50
x+y+x-y=50
2x=50
x=25

Therefore, we get the age of Q,but unable to find R and T's age because we cannot get the Y's value by any means.Hence data is inadequate to find the difference b/w R and Q's Age.

Roshan/Dev said: (Sep 1, 2012)  
Very good sweta and deepak. Excellently fantabulous.

Nitin K said: (Oct 13, 2012)  
If the diff between ages is same then it has to be
T<Q<R : 24<25<26.
and sum of T & R is 50 as per the data so the difference is 1.

option A is right.

Hassan said: (Oct 17, 2012)  
@Nitin.

Your wrong because the question just state that Q is as much younger than are as he is older than T, no more explanation to whether this youngness or oldness is by how many years. Thus why, option D is the right answer.

Vishranthee said: (Feb 9, 2013)  
R=Q-x

Q=T-x

R+T=50

So x(which is the difference between R and Q) is 25.

Neha Dugar said: (Mar 12, 2013)  
@Vishranthee.

Your answer is wrong.
The correct answer is D.

Now lets have a look,
R-Q=Q-T..........(1)

Then,
It is also given that, R+T=50.......(2)
From equation (1) we get R+T=2Q
that means Q=25.
Again,

We can write R-Q=Q-T.(From equation(1))
=25-T.

But we don't know the value of T.
So the given data is inadequate.

Laxman said: (Mar 20, 2013)  
Hi friends,

I think answer should be "E" because in last position answer becomes Q=25 AND R+T=50. So, as difference between T,Q and Q,R are same , option may be and should be 25 years each of T and R. So, AS A RESULT difference between R and Q is 0. And answer should be NONE OF THESE.

Jemeela Jain said: (Jul 3, 2013)  
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?

Aditia said: (Aug 23, 2013)  
according to the question:

Q-T = R-Q.
2Q = R+T....(1).

Also we know that R-T= 50...(2).

Solving these equations, we get:

2R = 2Q+50.
2R-2Q = 50.
R-Q = 25.

So the correct answer should be 25.

Red said: (Oct 19, 2013)  
Q and R are of the same age if you observe closely.

So Q = R.

R plus T is equal to 50 same as T plus Q.

Parmeshwar said: (Jan 1, 2014)  
Hi @Red,

Can you check this explanation :

According to question.

R + T = 50.

And 2Q = R + T = 50.
Therefore, Q = 25.

Also we know :

T+x = Q and T + 2x(R) =50 (given).

or

T + x = 25(Q).
T + 2x = 50.
------------
- - -
--------------
so x= 25.


So R - Q = 25.
Same as what @Aditya got :).

Ravinder said: (Aug 2, 2014)  
R+T = 50.
T = 50-R.....(1)
R-Q = Q-T.
R-T = 2Q.

FROM EQ.1,
R-(50-R) = 2Q.
2R-2Q = 50.
R-Q = 25.

Parveen Dhawan said: (Aug 5, 2014)  
R+T = 50.
T = 50-R.....(1)
R-Q = Q-T given.
R+T = 2Q.

Substituting the value of T from eq.1,
R+(50-R) = 2Q.
2Q = 50.
Q = 25.

Abc said: (Aug 17, 2014)  
Given,

R+T = 50 --(1).
R-Q = Q-T --(2).
T<Q<R.

Let us assume ages be 24, 25, 26
==> (2) 26-25 = 25-24.
(1) 26+24 = 50.

Hence option A.

Rohit Bansal said: (Aug 26, 2014)  
T = x-y.
Q = x.
R = x+y.

Hence R+T = 50, Q = 25 if Q = 25 then R = 27 and T = 23 because sum of R+T = 50 and condition of R and T as comparison Q

Hence answer is 2 years.

Shreyas said: (Oct 7, 2014)  
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.

Shilpa K R said: (Nov 1, 2014)  
@Rohit bansal.

Even though the answer is correct ,,these are not the only values which satisfy the equation
as you have mentioned .

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

x-y+x+y = 50.
2x = 50.
x = 25.

which makes Q as 25.

if y is 1 then T = 24 and R = 26.

if y is 2 then T = 23 and R = 27 and so on :).

Yogi said: (Feb 26, 2015)  
Guys there are so many answers which can be true but we can't determine the exact answer. So answer is (D) data inadequate.

Sudheer said: (Mar 26, 2015)  
Can anyone explain why they took r-q = q-t? In the question they didn't gave as equal.

Ramnaresh said: (Apr 3, 2015)  
Data inadequate is the answer because q=25.

We all knew but r+t=50.

So r may be 40 and t may be 10, r may be 35 and t may be 15.

We get answers so the answer will be D.

Vicz said: (Jul 28, 2015)  
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.

Mounika said: (Aug 15, 2015)  
The difference of age b/w R and Q = The difference of age b/w Q and T.

Where is this given in question?

Rithu said: (Mar 2, 2016)  
Same doubt here.

Pinky said: (Apr 1, 2016)  
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.)

Purnendu Paul said: (Sep 18, 2016)  
Answer is : A.

Since, Q is 25yrs. And in the question given that, the sum of R & T is 50yrs. and Q is as older as younger than T and R. So, taking 1 we can get T is(25 + 1) = 26yrs. and R is (25 - 1) = 24yrs. Where, 24 + 26 = 50yrs. ( i.e. R + T = 50yrs.).

There is no other number rather than 1 by which we can get 50, where Q is 25yrs.

Purnendu Paul said: (Sep 18, 2016)  
Hello @Mounika.

Read the first sentence carefully, then you will get the concept clearly.

Pritiparna said: (Oct 9, 2016)  
Ans.
R = 1
Q = 25
T = 49.

(the difference between the ages of these three is 24, and the sum of the ages of R and T is 50)

Davinder said: (Nov 18, 2016)  
Answer:

T = 24
O = 25
R = 26

Smrithi said: (Jan 17, 2017)  
R-Q = Q+T;--------------------------GIVEN DATA
R+T = 50;----------------------------1
R-T = 2Q;----------------------------2
T = 50-R;
Substitute in 2.
R - (50 - R) = 2Q;
2R-2Q = 50;
R-Q = 25;

So, OPTION D.

Hemant said: (Feb 1, 2017)  
Here we check with 15, 25, 35 so,

35 + 15 = 50, and 25 - 15 = 35 - 25 = 10. Here we get all the ages.

Alam said: (Apr 17, 2017)  
Can anybody explain how R-Q=Q-T?

Yogeshree said: (Jun 23, 2017)  
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.

Mubarak said: (Aug 16, 2017)  
It's given that Q is as much younger than R as he is older than T.
so if is 15 then Q-T = 10;
Q+10 =35 =R.
its given that R+T =50 ==> 35+15 = 50.
so R-Q = 35-25 = 10.

Saiful Islam said: (Oct 16, 2017)  
If I let T=x, also let, are will be 2 years older than T and Q will be x.

Also details:.

T=x.
R=x+2.
Q= x+2-2=x.

According to question,

X+2+x=50.
=> x = 24.

So, are is = 26.

Q= 24.
R-Q= 26-24= 2 Years.

Please tell me is it right or wrong.

Dnyanesh said: (Nov 8, 2017)  
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.

Manohar said: (Feb 18, 2018)  
Q is as much younger than R as he is older than T.

R-Q=Q+T
younger than is - and older than is+
so,
R-T=2Q ------> (1)
and given R+T=50 ------> (2)
SOLVE 1&2 Eqns, we get
2R=50+2Q
Therefore R-Q= 25.

Please tell me is it right or wrong.

Abc said: (Aug 30, 2018)  
Correct, thanks @Manohar.

Elowrajite said: (Oct 16, 2018)  
This answer should be 'E' as specify in question because Q is as much younger than are as he is older than T. And sum of the ages of are and T is 50 years,
R+T=50.
To consider R=40 and T=10 to make it coherent with Q.
Say Q=25 which is 15 years younger than is as is 15 years older than T.

Hope you understand.

Anomie said: (Feb 14, 2019)  
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.

Rana Sultan said: (Mar 7, 2019)  
T < Q < R.
x 2x 3x.

Now,
R+T = 50,
3x + x = 50,
4x = 50,
x=12.5 ---> T
So, 2x = 25 ---> Q
And 3x =37.5 ---> R

R-Q = 37.5- 25 = 12.5 is the answer.

Savitha said: (May 25, 2019)  
Can anybody explain how R-Q = Q-T?

Pavan said: (Jul 13, 2019)  
20,25,30 consider and calculate.
So, the Answer will be 10 years.

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