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 _____________.

Correct Answer: Option C (W)

Let us solve the floor puzzle step-by-step to find the exact arrangement of all 10 persons on floors 1 to 10.

Step 1: Determine the positions of V, S, and P.
1. "V lives on prime numbered floor but below 4th floor."
The floors below 4th floor are 1, 2, and 3. The prime numbers in this set are 2 and 3. So, V can live on floor 2 or floor 3.
2. "S lives below V but not on the ground floor (floor 1)."
Since S must live below V and S cannot be on floor 1, V MUST live on floor 3, and S MUST live on floor 2.
3. "There are as many persons live above S as below P."
S is on floor 2, so there are 10 - 2 = 8 persons living above S.
Therefore, there must be 8 persons living below P. This places P on floor 9.

Step 2: Determine the positions of Y, T, X, R, and W.
1. "More than three persons live between P and Y who lives above X."
P is on floor 9. Since more than 3 persons (at least 4 persons) live between P and Y, and Y lives below P, Y can be on floor 4 or lower.
2. "One person lives between T and Y."
3. "W lives just below R." (R and W must be on consecutive floors: R directly above W).
4. "Y lives above X."

Let's test the placement of Y:
If Y is on floor 4:
- Between P (9) and Y (4), there are 4 floors (8, 7, 6, 5), which satisfies "more than three persons".
- One person between T and Y: T could be on floor 6 or floor 2. But floor 2 is occupied by S. So T must be on floor 6.
- We need two adjacent empty floors for R and W (R on top of W).
Currently filled: Floor 9 (P), Floor 6 (T), Floor 4 (Y), Floor 3 (V), Floor 2 (S).
Available floors: 10, 8, 7, 5, 1.
The adjacent empty floors available are 8 and 7. So R is on floor 8 and W is on floor 7.
- Now available floors left: 10, 5, 1.
- "U does not live below Q" means U lives above Q.
- "Y lives above X", so X must be below Y. The only floor below Y (floor 4) that is empty is floor 1. So X is on floor 1.
- Remaining empty floors are 10 and 5. Since U lives above Q, U is on floor 10 and Q is on floor 5.

Step 3: Verify the full arrangement from floor 10 to floor 1:
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

Step 4: Answer the given question.
Question: "The numbers of persons live between R and Y is half than the numbers of persons live below _____________."
- Persons between R (floor 8) and Y (floor 4) are W, T, and Q, which is 3 persons.
- 3 is half of 6.
- So we need to find the person who has 6 persons living below them.
- The person on floor 7 (W) has 6 persons living below them (floors 1, 2, 3, 4, 5, and 6).

Therefore, the number of persons between R and Y (3) is half the number of persons who live below W (6).