Aptitude - Problems on Ages - Discussion

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

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.

From above question:

Given,
R - Q = Q - T ------> 1st condition
R + T = 50 ------> 2nd condition
With this, we can find Q,
R - Q = Q - T.
R + T = 2Q,
2Q = 50,
Q = 25.

With the help of condition 1,

We know that the difference between R and Q,Q and T were same, consider it as 'x'. i.e., T=Q-x, R=Q+x.

Now consider T=1 year,
Then the difference between Q and T is (25-1)years i.e., x=24 years.
Then R =Q+x= 25+24= 49 years.

Check it satisfies both of the conditions.
R + T = 50.
R - Q = Q-T.

Now the difference between R and Q is (49-25).
= 24 years.

From above question:

Given,
R-Q = Q - T -------> 1st condition
R+T = 50 -------> 2nd condition.
With this, we can find Q,
R-Q = Q-T
R+T = 2Q
2Q = 50
Q = 25.

with the help of condition 1,

We know that the difference between R and Q,Q and T were the same, consider it as 'x'. i.e., T=Q-x, R=Q+x.

Now consider T=1 year,
Then the difference between Q and T is (25-1)years i.e., x=24 years.
Then R = Q + x= 25 + 24 = 49 years.

Check it satisfies both of the conditions.......
R+T=50
R-Q=Q-T

Now the difference between R and Q is (49-25)
= 24 years

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.

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.

Why here,
R-Q = Q-T?

Please explain.

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

The answer is 25,

Then, Why D is correct?

Anyone, explain me the correct answer.