Aptitude - Problems on Ages - Discussion

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.

Here I have done a reverse method to find answer.

So according to question T is the youngest one then Q and then R.
So if we consider T = x.

And try options in it.
First ans is 1 year difference, if this is right then Q=x+1 and R = x+2

Question says,
T+R = 50.
x+x+2= 50.
x= 24.
x=T.

Therefore, T= 24years.
Q=25.
R=26.

Then this fulfil both the criteria of age difference as well as the sum total of R and T.
Therefore option A: year is right.

If I let T=x, also let, are will be 2 years older than T and Q will be x.

Also details:.

T=x.
R=x+2.
Q= x+2-2=x.

According to question,

X+2+x=50.
=> x = 24.

So, are is = 26.

Q= 24.
R-Q= 26-24= 2 Years.

Please tell me is it right or wrong.

It's given that Q is as much younger than R as he is older than T.
so if is 15 then Q-T = 10;
Q+10 =35 =R.
its given that R+T =50 ==> 35+15 = 50.
so R-Q = 35-25 = 10.

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?

Here we check with 15, 25, 35 so,

35 + 15 = 50, and 25 - 15 = 35 - 25 = 10. Here we get all the ages.

R-Q = Q+T;--------------------------GIVEN DATA
R+T = 50;----------------------------1
R-T = 2Q;----------------------------2
T = 50-R;
Substitute in 2.
R - (50 - R) = 2Q;
2R-2Q = 50;
R-Q = 25;

So, OPTION D.

Answer:

T = 24
O = 25
R = 26

Ans.
R = 1
Q = 25
T = 49.

(the difference between the ages of these three is 24, and the sum of the ages of R and T is 50)