How many persons are living between the floors on which P and T lives?

From (i), it is clear that both Q and U are on even numbered floor and since, U is on 2^{nd}floor, only 4^{th},6^{th} and 8^{th} floor are there for Q and Y. Since, Y is not above Q, there are two possibilities: Possibility (a) – Q at 8^{th}and Y at 6^{th}floor. Possibility (b) – Q at 6^{th}and Y at 4^{th}floor. But statement (ii) says, that one who likes white lives on 4^{th}floor and Y does not like white, possibility (b) is not possible. Hence, we will go with possibility (a) which is Q at 8^{th}(likes Violet) and Y at 6^{th}floor. Statement (ii) also says that person on 3rd floors likes Yellow. From (iii), it is clear that the person who likes pink is on the 5^{th}floor. From (vii), we can say that the person who likes red is on the 9^{th}floor and also the person who likes purple lives on the 6^{th}floor . From (v), T is not on the 1^{st}floor and also since he does not like Yellow, he is not on the 3^{rd}floor. From (iv), neither W nor R can be at the 9^{th}floor, as W likes green and R is not at the topmost floor. Also as W likes green, only two floors .i.e 7^{th}and 1^{st}, are left for W. Hence, there are two possibilities for W and R : Possibility (a) – W at 7^{th}floor and R at 3^{rd}floor. Possibility (b) - R at 5^{th}floor and W at 1^{st}floor. But we can see in the above table that T cannot be at 1^{st}or 3^{rd}floor. Now (vi), says that there is one floor between the floor on which T and R live. Hence, R also cannot be at 3^{rd}floor. Therefore, possibility (a) cannot be correct. Hence, we will go ahead with the possibility (b) which is R at 5^{th}and W at 1^{st}floor and also from (vi), it is clear that T will be on the 7^{th}floor. Only colourBlack is left for T, hence T likes Black. From (vi), it is also clear that V and P will be on 4^{th}and 3^{rd}floors respectively. Now only person left for 9^{th}floor is X. Final arrangement will be as follows:

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