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

? : 3839 :: 11 : 1209

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

What does below Rebus say?

XLR8

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

When is the top of a mountain similar to a savings account?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

What begins with T, ends with T, and has T in it?

Yesterday I fell from 30 feet high ladder but I don't get hurt. Why?