Aptitude - Problems on Ages - Discussion

Here q=t
So, r+t=50 therefore q=25.
So, t = 25.

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.

Why here,
R-Q = Q-T?

Please explain.

Q-x = R
R + x = T ---> (i)
R + T = 50
R + R + x = 50 --> from(i)
2R + x = 50.
Therefore the age of R is not given hence option E.

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.

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

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.

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.