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.
Laxman said:
1 decade ago
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.
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:
1 decade ago
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?
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:
1 decade ago
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.
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:
1 decade ago
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.
So Q = R.
R plus T is equal to 50 same as T plus Q.
Parmeshwar said:
1 decade ago
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 :).
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:
1 decade ago
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.
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:
1 decade ago
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.
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:
1 decade ago
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.
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:
1 decade ago
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.
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:
1 decade ago
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.
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.
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