Aptitude - Problems on Ages - Discussion

Let's say Q = R - x.
So Q=T + x.

Adding these 2 we will get;
2Q = R + T.
So 2Q = 50,
And Q = 25.

We can find R =27 by substituting Q and difference is 2 years.

The answer is 10 years because the given condition is possible for q=25,
R=35.

And
T = 15.

Given,
R+T = 50,
R - Q = Q -T.
Now,
2Q = R + T.
2Q = 50.
Q = 25.

Now we can have the following options:

R-Q-T
30-25-20
35-25-15
40-25-10
45-25-5

So the difference between R and Q is either 5, 10, 15, 20.

We can say that the data is not sufficient to claim the definite difference.

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.

20,25,30 consider and calculate.
So, the Answer will be 10 years.

Can anybody explain how R-Q = Q-T?

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.

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.

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.

Correct, thanks @Manohar.