Study the following information carefully and answer the questions given below:

Ten persons P to Y live in 10 storey building but not necessarily in the same order. The bottommost floor is numbered as 1 and so on till the topmost floor is numbered as 10.

V lives on prime numbered floor but below 4th floor. S lives below V but not on the ground floor. There are as many persons live above S as below P. More than three persons live between P and Y who lives above X. One person lives between T and Y. W lives just below R. U does not live below Q.

The numbers of persons live between R and Y is half than the numbers of persons live below _____________.

The correct answer is W.

Let us solve the puzzle step-by-step to find the arrangement of the ten persons (P to Y) on the 10 floors (numbered 1 to 10 from bottom to top):

Step 1: Determine the positions of V and S.
V lives on a prime numbered floor below the 4th floor. The prime floors below 4 are 2 and 3.
S lives below V but not on the ground floor (floor 1).
If V were on floor 2, S would have to live on floor 1, which is not possible as S cannot be on the ground floor.
Therefore, V must live on floor 3, and S must live on floor 2.

Step 2: Find the position of P.
There are as many persons living above S as below P.
Since S is on floor 2, the number of floors above S is:
$10-2=8$
Thus, there must be 8 floors below P, which means P lives on floor 9.

Step 3: Determine the positions of Y and X.
More than three persons live between P (floor 9) and Y. This means there are at least 4 floors between P and Y.
So, the floor of Y must be floor 4 or lower.
Since floors 3 (V) and 2 (S) are already occupied, Y can only be on floor 4 or floor 1.
However, Y lives above X. Since X must live on a floor lower than Y, Y cannot live on floor 1.
Therefore, Y lives on floor 4, and X lives on floor 1.

Step 4: Find the position of T.
One person lives between T and Y (floor 4).
This means T could live on floor 6 or floor 2.
Since S lives on floor 2, T must live on floor 6.

Step 5: Position R and W.
W lives just below R. This means R and W live on adjacent floors (R above W).
Let's check the remaining vacant floors: floors 10, 8, 7, and 5.
The only adjacent vacant floors are floors 8 and 7.
Therefore, R lives on floor 8, and W lives on floor 7.

Step 6: Place U and Q.
The remaining vacant floors are 10 and 5.
Since U does not live below Q (meaning U lives above Q), U must live on floor 10, and Q lives on floor 5.

Summary of the final floor arrangement:
Floor 10: U
Floor 9: P
Floor 8: R
Floor 7: W
Floor 6: T
Floor 5: Q
Floor 4: Y
Floor 3: V
Floor 2: S
Floor 1: X

Answering the question:
The number of persons living between R (floor 8) and Y (floor 4) is 3 (persons living on floors 7, 6, and 5).
According to the question, this number (3) is half the number of persons living below a certain person.
Therefore, the number of persons living below that person must be:
$3\times 2=6$
The person who has exactly 6 floors below them lives on floor 7. Looking at our final arrangement, W lives on floor 7.