Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

If eleven plus two equals one, what does nine plus five equal?

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

What can you deduce from the following BrainBat?

CRY
LMKI

Who always enjoys poor health?

There is a family that live in a round house. The two parents go out for a movie and leave a babysitter to watch their son. They come back and the kid was not there. Some one kidnapped him. The maid said she was cleaning in a corner. The cook said he was making pizza. The babysitter said she was getting a board game. Who kidnapped him.

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

I am white when I am dirty, and black when I am clean. What am I?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?