Aptitude - Problems on Ages - Discussion

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.

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.

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

And
T = 15.

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.

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

The answer is 25,

Then, Why D is correct?

Anyone, explain me the correct answer.