Aptitude - Problems on Ages - Discussion
Discussion Forum : Problems on Ages - General Questions (Q.No. 14)
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?
Answer: Option
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.
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.
Discussion:
60 comments Page 2 of 6.
Mohamed Abdul Raseeth said:
4 years ago
Actually, in this question, three options are correct i.e A, B, C. Hence we can say the data is inadequate.
Since, Q is younger than R as such Q is older than T.
Q = T+x.
R = Q+x.
Hence, R - Q = Q - T
R+T = 2Q,
R+T = 50 (Given),
2Q = 50,
Q = 25.
ACCORDING TO QUESTION,
R>Q>T.
Hence the possibilities are;
R = 50
Q = 25.
T=0., IN THIS CASE R - Q=25.
2) R=26.
Q=25.
T=24, R-Q=1.
3)R=27.
Q=25.
T=23, R-Q=2.
4)R=35.
Q=25.
T=15, R-Q=10.
Since, Q is younger than R as such Q is older than T.
Q = T+x.
R = Q+x.
Hence, R - Q = Q - T
R+T = 2Q,
R+T = 50 (Given),
2Q = 50,
Q = 25.
ACCORDING TO QUESTION,
R>Q>T.
Hence the possibilities are;
R = 50
Q = 25.
T=0., IN THIS CASE R - Q=25.
2) R=26.
Q=25.
T=24, R-Q=1.
3)R=27.
Q=25.
T=23, R-Q=2.
4)R=35.
Q=25.
T=15, R-Q=10.
(4)
Deepak Varshney said:
1 decade ago
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.
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.
Nafees Javed said:
5 years ago
Q=25 years.
According to the question.
Q is as much younger than R as he is older than T.
R+T = 50 years.
If we add their values then;
R + T + Q = 75 years.
And
Q is as much younger than R as he is older than T. (According to the question).
It is possible that,
R=26,
Q=25 (Younger than R by 1 year),
T=24 (Older than T by 1 year).
Option A may be the correct answer
According to the question.
Q is as much younger than R as he is older than T.
R+T = 50 years.
If we add their values then;
R + T + Q = 75 years.
And
Q is as much younger than R as he is older than T. (According to the question).
It is possible that,
R=26,
Q=25 (Younger than R by 1 year),
T=24 (Older than T by 1 year).
Option A may be the correct answer
Wgn said:
1 decade ago
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
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
Vinay Thorat said:
5 years ago
As the question says, Q is as much younger than R as he is older than T.
It means R-----(x)----Q----(x)----(T).
If T and R having the sum of 50, then,
Let say, age of R=1yrs and T=49 yrs. Then R+T=50.
So, R=1yrs.
Q=R+x=1+24=25 yrs.
T=Q+x=25+24=49 yrs.
so we can say, the difference between R and Q's age will be 24.
So, None of the Above options is right.
It means R-----(x)----Q----(x)----(T).
If T and R having the sum of 50, then,
Let say, age of R=1yrs and T=49 yrs. Then R+T=50.
So, R=1yrs.
Q=R+x=1+24=25 yrs.
T=Q+x=25+24=49 yrs.
so we can say, the difference between R and Q's age will be 24.
So, None of the Above options is right.
Purnendu Paul said:
9 years ago
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.
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.
Neha Dugar said:
1 decade ago
@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.
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.
Elowrajite said:
7 years ago
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.
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.
Shilpa k r said:
1 decade ago
@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 :).
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 :).
Likhit Naik said:
6 years ago
Given,
R+T = 50,
R - Q = Q -T.
Now,
2Q = R + T.
2Q = 50.
Q = 25.
NOW,
R + T = 50.
Assume R = 30 & T = 20.
Substitute in
R - Q = Q - T.
30 - 25 = 25 - 20.
L.H.S = R.H.S.
NOW R = 30.
SO,
R - Q = 5.
Hence answer is option E.
None of the above.
R+T = 50,
R - Q = Q -T.
Now,
2Q = R + T.
2Q = 50.
Q = 25.
NOW,
R + T = 50.
Assume R = 30 & T = 20.
Substitute in
R - Q = Q - T.
30 - 25 = 25 - 20.
L.H.S = R.H.S.
NOW R = 30.
SO,
R - Q = 5.
Hence answer is option E.
None of the above.
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