Question

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
(a) 1 year
(b) 2 years
(c) 25 years
(d) Data inadequate
(e) None of these

Answer 1

Hint:In this question, we first need to write the equation that the difference between age of R and Q will be the same as the difference of age of Q and T. Then as given that the sum of the age of R and T is 50 years. Now, on substituting this value in the above relation we get the age of Q. Then on further simplification we get the result.

Complete step-by-step answer:
Let us assume that the age of Q as x, age of R as y and the age of T as z.
Now, as given in the question, the difference between the age of Q and R is the same as the difference between the age of R and T.
Now, on substituting the respective values and writing the equation we get,\
\[\Rightarrow y-x=x-z\]
Now, on rearranging the terms in the above equation we get,
\[\Rightarrow y+z=x+x\]
Now, this can also be written as
\[\Rightarrow y+z=2x.....\left( 1 \right)\]
As already given in the question, the sum of the age of R and T is 50 years.
Now, we can write it as
\[\Rightarrow y+z=50\]
Let us now substitute the value in the above equation (1)
\[\Rightarrow y+z=2x\]
Now, on substituting the value we get,
\[\Rightarrow 50=2x\]
Let us now divide with 2 on both sides,
\[\begin{align}
  & \Rightarrow \dfrac{50}{2}=x \\
 & \therefore x=25years \\
\end{align}\]
Now, we need to find the value of \[y-x\]
We cannot find the value of \[y-x\] as we only know the value of x.
Hence, the correct option is (d).

Note:While writing the equation for the given relation between the ages of Q, R, T from the question it is important to note that we subtract x from y but not y from x because Q is younger than R.It is also important to note that we equate that difference of Q and R to the difference of Q and T in which z is subtracted from x as Q is older than T. It means that age of Q is greater than T.Altering the terms in the subtraction or neglecting any of the terms changes the result completely. Also as there are 3 variables and only two equations we cannot get the value of y. Hence, the answer cannot be found from the data given.