Good one ..
Conditions
1) each one has different colours
2) Exactly one of the statement can be correct

My arguments is like this
If X is Red is True then Y is not Red will also be true which violates second condition .
So X is RED not possible
Hence X cannot be true ( so X is White or Blue)

Now Y is not Red is True imply Y is White or Blue
Suppose Y is Blue then third statement will be True Not possible
Y is White then X will become Blue again third statement also become true.
Hence Y is not red is False So Y is RED...
Z can be White or Blue But since only one statement is True Z is Blue Hence X is White
X=White
Y= Red
Z= Blue

Good one ..

Conditions

1) each one has different colours

2) Exactly one of the statement can be correct

My arguments is like this

If X is Red is True then Y is not Red will also be true which violates second condition .

So X is RED not possible

Hence X cannot be true ( so X is White or Blue)

Now Y is not Red is True imply Y is White or Blue

Suppose Y is Blue then third statement will be True Not possible

Y is White then X will become Blue again third statement also become true.

Hence Y is not red is False So Y is RED...

Z can be White or Blue But since only one statement is True Z is Blue Hence X is White

X=White

Y= Red

Z= Blue